sunyiyou/math_combinatory_distribution_level_2

messages listlengths 1 1	ground_truth stringclasses 11 values	dataset stringclasses 1 value
[ { "content": "Distribute the letters {'v': 3, 'o': 1, 'y': 2} among 3 distinguishable boxes with capacities [2, 3, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "Given the letters {'c': 1, 'z': 1, 'x': 4}, place them into 3 labeled boxes with sizes [2, 1, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	8	MATH
[ { "content": "Arrange the letters {'q': 3, 'j': 2, 'l': 1} into 3 undistinguishable boxes with capacities [2, 2, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	3	MATH
[ { "content": "You have {'u': 2, 'w': 2, 'b': 2} and need to distribute them into 3 different boxes with capacities [2, 2, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	21	MATH
[ { "content": "Arrange the letters {'b': 2, 's': 3, 'c': 1} into 3 undistinguishable boxes with capacities [2, 2, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	3	MATH
[ { "content": "You have {'h': 1, 'a': 2, 'y': 3} and need to distribute them into 3 different boxes with capacities [2, 3, 1]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "Divide the letters from {'l': 2, 'u': 2, 'w': 2} into 3 undistinguishable boxes with sizes [2, 2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	5	MATH
[ { "content": "Distribute the letters {'i': 1, 'n': 1, 'o': 4} among 3 distinguishable boxes with capacities [3, 1, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	8	MATH
[ { "content": "Arrange the letters {'w': 1, 'v': 2, 'f': 3} into 3 undistinguishable boxes with capacities [1, 3, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "You have {'c': 2, 'a': 3, 'k': 1} and need to distribute them into 3 identical boxes with capacities [2, 2, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	3	MATH
[ { "content": "Given the letters {'w': 2, 'a': 3, 'g': 1}, place them into 3 labeled boxes with sizes [3, 1, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "You have {'z': 1, 'r': 3, 's': 2} and need to distribute them into 3 different boxes with capacities [1, 4, 1]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	8	MATH
[ { "content": "Arrange the letters {'i': 3, 'a': 1, 'j': 2} into 3 uniquely identified boxes that can hold [2, 2, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	15	MATH
[ { "content": "Given the letters {'o': 3, 'h': 2, 'c': 1}, place them into 3 labeled boxes with sizes [2, 2, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	15	MATH
[ { "content": "Arrange the letters {'t': 4, 'd': 1, 'e': 1} into 3 uniquely identified boxes that can hold [3, 1, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	8	MATH
[ { "content": "Distribute the letters {'h': 1, 'o': 2, 'v': 3} among 3 distinguishable boxes with capacities [1, 2, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "Distribute the letters {'h': 3, 'z': 1, 'a': 2} among 3 distinguishable boxes with capacities [2, 3, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "Given the letters {'t': 1, 'u': 1, 'd': 4}, place them into 3 labeled boxes with sizes [2, 2, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	9	MATH
[ { "content": "Divide the letters from {'d': 1, 'e': 3, 'b': 2} into 3 undistinguishable boxes with sizes [3, 1, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "Divide the letters from {'k': 2, 'd': 1, 'e': 3} into 3 undistinguishable boxes with sizes [3, 1, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "Distribute the letters {'v': 2, 't': 1, 'h': 3} among 3 identical containers that can hold [2, 1, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "Distribute the letters {'l': 3, 'h': 1, 'x': 2} among 3 distinguishable boxes with capacities [2, 2, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	15	MATH
[ { "content": "Given the letters {'k': 3, 'c': 2, 'q': 1}, place them into 3 indistinguishable boxes with sizes [3, 2, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "Distribute the letters {'h': 3, 'n': 2, 'c': 1} among 3 distinguishable boxes with capacities [2, 3, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "Arrange the letters {'d': 2, 'e': 1, 'j': 3} into 3 uniquely identified boxes that can hold [1, 2, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "Arrange the letters {'g': 4, 'b': 1, 'c': 1} into 3 undistinguishable boxes with capacities [2, 1, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	8	MATH
[ { "content": "Arrange the letters {'v': 1, 'x': 2, 'z': 3} into 3 uniquely identified boxes that can hold [1, 1, 4] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	8	MATH
[ { "content": "Divide the letters from {'q': 1, 't': 3, 'w': 2} into 3 undistinguishable boxes with sizes [4, 1, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	5	MATH
[ { "content": "Given the letters {'b': 2, 'a': 2, 'e': 2}, place them into 3 indistinguishable boxes with sizes [1, 2, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	15	MATH
[ { "content": "Distribute the letters {'o': 2, 'r': 2, 'm': 2} among 3 identical containers that can hold [2, 2, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	5	MATH
[ { "content": "Given the letters {'g': 2, 'i': 2, 'b': 2}, place them into 3 labeled boxes with sizes [3, 1, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	15	MATH
[ { "content": "Divide the letters from {'c': 3, 'j': 2, 'h': 1} into 3 distinctively labeled boxes with sizes [2, 1, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "You have {'s': 2, 'm': 3, 'g': 1} and need to distribute them into 3 different boxes with capacities [3, 1, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "Divide the letters from {'r': 2, 'f': 3, 'q': 1} into 3 undistinguishable boxes with sizes [1, 1, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	5	MATH
[ { "content": "Arrange the letters {'o': 2, 'f': 1, 'j': 3} into 3 undistinguishable boxes with capacities [1, 2, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "Divide the letters from {'y': 1, 'f': 1, 'c': 4} into 3 undistinguishable boxes with sizes [3, 1, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	8	MATH
[ { "content": "Arrange the letters {'q': 3, 'm': 2, 'o': 1} into 3 undistinguishable boxes with capacities [4, 1, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	5	MATH
[ { "content": "Given the letters {'i': 2, 'l': 1, 'v': 3}, place them into 3 indistinguishable boxes with sizes [3, 1, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "Divide the letters from {'p': 2, 'h': 2, 'z': 2} into 3 distinctively labeled boxes with sizes [2, 2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	21	MATH
[ { "content": "Distribute the letters {'r': 3, 't': 2, 'u': 1} among 3 identical containers that can hold [2, 2, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	3	MATH
[ { "content": "Given the letters {'e': 2, 'h': 2, 'c': 2}, place them into 3 indistinguishable boxes with sizes [2, 2, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	5	MATH
[ { "content": "Given the letters {'q': 3, 'g': 2, 'p': 1}, place them into 3 labeled boxes with sizes [1, 1, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	8	MATH
[ { "content": "Given the letters {'f': 1, 'q': 3, 'o': 2}, place them into 3 indistinguishable boxes with sizes [2, 2, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	3	MATH
[ { "content": "Given the letters {'o': 2, 'g': 1, 'j': 3}, place them into 3 labeled boxes with sizes [1, 2, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "Given the letters {'b': 1, 'v': 2, 'w': 3}, place them into 3 labeled boxes with sizes [1, 2, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "Given the letters {'l': 2, 'v': 2, 'd': 2}, place them into 3 indistinguishable boxes with sizes [3, 2, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	15	MATH
[ { "content": "Arrange the letters {'r': 1, 'o': 3, 'j': 2} into 3 uniquely identified boxes that can hold [3, 1, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "Distribute the letters {'c': 1, 'r': 2, 'm': 3} among 3 distinguishable boxes with capacities [2, 3, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "Given the letters {'f': 2, 'n': 1, 'l': 3}, place them into 3 labeled boxes with sizes [3, 1, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "You have {'v': 3, 'b': 2, 'o': 1} and need to distribute them into 3 identical boxes with capacities [3, 1, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "Distribute the letters {'k': 2, 's': 3, 'y': 1} among 3 distinguishable boxes with capacities [3, 1, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "You have {'e': 2, 'd': 3, 'v': 1} and need to distribute them into 3 identical boxes with capacities [2, 2, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	3	MATH
[ { "content": "Distribute the letters {'u': 3, 'y': 1, 'k': 2} among 3 identical containers that can hold [2, 2, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	3	MATH
[ { "content": "Divide the letters from {'s': 2, 'n': 2, 'p': 2} into 3 distinctively labeled boxes with sizes [2, 2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	21	MATH
[ { "content": "Arrange the letters {'w': 2, 'p': 1, 'f': 3} into 3 undistinguishable boxes with capacities [1, 2, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "Arrange the letters {'b': 2, 's': 1, 'k': 3} into 3 uniquely identified boxes that can hold [2, 1, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "Arrange the letters {'i': 1, 'z': 4, 'm': 1} into 3 undistinguishable boxes with capacities [1, 3, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	8	MATH
[ { "content": "Distribute the letters {'m': 3, 'l': 1, 'h': 2} among 3 distinguishable boxes with capacities [2, 2, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	15	MATH
[ { "content": "Divide the letters from {'j': 3, 'k': 2, 'r': 1} into 3 undistinguishable boxes with sizes [1, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "Divide the letters from {'i': 2, 'q': 1, 'o': 3} into 3 distinctively labeled boxes with sizes [1, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "Given the letters {'y': 1, 'h': 2, 'z': 3}, place them into 3 labeled boxes with sizes [1, 3, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "Given the letters {'e': 2, 'd': 1, 'u': 3}, place them into 3 labeled boxes with sizes [1, 4, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	8	MATH
[ { "content": "You have {'w': 2, 'q': 3, 'p': 1} and need to distribute them into 3 different boxes with capacities [1, 4, 1]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	8	MATH
[ { "content": "Distribute the letters {'h': 3, 'z': 1, 'j': 2} among 3 distinguishable boxes with capacities [3, 1, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "You have {'g': 2, 'j': 2, 'y': 2} and need to distribute them into 3 identical boxes with capacities [3, 2, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	15	MATH
[ { "content": "You have {'i': 1, 'n': 2, 'v': 3} and need to distribute them into 3 different boxes with capacities [2, 2, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	15	MATH
[ { "content": "Given the letters {'f': 2, 'k': 1, 'y': 3}, place them into 3 labeled boxes with sizes [2, 3, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "Distribute the letters {'d': 1, 'f': 3, 'h': 2} among 3 identical containers that can hold [1, 1, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	5	MATH
[ { "content": "Distribute the letters {'t': 3, 'g': 2, 'p': 1} among 3 identical containers that can hold [2, 2, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	3	MATH
[ { "content": "Divide the letters from {'y': 2, 'm': 2, 'c': 2} into 3 undistinguishable boxes with sizes [1, 4, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	6	MATH
[ { "content": "Arrange the letters {'z': 1, 'b': 2, 'x': 3} into 3 undistinguishable boxes with capacities [1, 3, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "Arrange the letters {'q': 2, 'b': 3, 'o': 1} into 3 uniquely identified boxes that can hold [2, 1, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "You have {'l': 2, 'b': 1, 'w': 3} and need to distribute them into 3 different boxes with capacities [1, 3, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "Distribute the letters {'h': 4, 'z': 1, 'b': 1} among 3 distinguishable boxes with capacities [1, 3, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	8	MATH
[ { "content": "Given the letters {'a': 4, 'h': 1, 'n': 1}, place them into 3 indistinguishable boxes with sizes [2, 2, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	2	MATH
[ { "content": "Given the letters {'j': 3, 'h': 1, 'w': 2}, place them into 3 indistinguishable boxes with sizes [2, 2, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	3	MATH
[ { "content": "Divide the letters from {'d': 3, 'l': 1, 'e': 2} into 3 undistinguishable boxes with sizes [4, 1, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	5	MATH
[ { "content": "You have {'f': 1, 'j': 2, 'v': 3} and need to distribute them into 3 different boxes with capacities [2, 2, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	15	MATH
[ { "content": "Given the letters {'g': 1, 'w': 2, 'y': 3}, place them into 3 indistinguishable boxes with sizes [1, 3, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "Divide the letters from {'g': 1, 'q': 2, 'y': 3} into 3 distinctively labeled boxes with sizes [2, 2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	15	MATH
[ { "content": "Divide the letters from {'t': 1, 'c': 3, 'q': 2} into 3 distinctively labeled boxes with sizes [1, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "Distribute the letters {'g': 2, 'e': 2, 'c': 2} among 3 distinguishable boxes with capacities [2, 1, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	15	MATH
[ { "content": "Distribute the letters {'a': 1, 'd': 3, 'g': 2} among 3 distinguishable boxes with capacities [1, 3, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "Divide the letters from {'d': 2, 'p': 1, 'r': 3} into 3 distinctively labeled boxes with sizes [1, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "Arrange the letters {'k': 2, 'g': 2, 'i': 2} into 3 undistinguishable boxes with capacities [2, 1, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	15	MATH
[ { "content": "Arrange the letters {'u': 1, 't': 1, 'r': 4} into 3 undistinguishable boxes with capacities [1, 4, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	4	MATH
[ { "content": "Arrange the letters {'l': 1, 'g': 2, 'u': 3} into 3 uniquely identified boxes that can hold [2, 1, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "You have {'y': 3, 'z': 2, 'i': 1} and need to distribute them into 3 identical boxes with capacities [1, 2, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "Given the letters {'k': 1, 'l': 3, 'e': 2}, place them into 3 indistinguishable boxes with sizes [1, 2, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "Divide the letters from {'l': 3, 'b': 1, 'c': 2} into 3 undistinguishable boxes with sizes [2, 1, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "Divide the letters from {'o': 2, 'x': 2, 'd': 2} into 3 undistinguishable boxes with sizes [1, 1, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	6	MATH
[ { "content": "Given the letters {'n': 2, 'h': 3, 'g': 1}, place them into 3 labeled boxes with sizes [2, 2, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	15	MATH
[ { "content": "Given the letters {'x': 2, 'n': 1, 's': 3}, place them into 3 indistinguishable boxes with sizes [2, 1, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "Arrange the letters {'a': 3, 'd': 2, 'x': 1} into 3 uniquely identified boxes that can hold [2, 2, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	15	MATH
[ { "content": "Given the letters {'f': 2, 'c': 2, 'y': 2}, place them into 3 labeled boxes with sizes [2, 3, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	15	MATH
[ { "content": "Given the letters {'f': 4, 'v': 1, 's': 1}, place them into 3 labeled boxes with sizes [1, 1, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "Given the letters {'x': 3, 'l': 1, 'j': 2}, place them into 3 indistinguishable boxes with sizes [3, 2, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "Given the letters {'o': 1, 'j': 3, 'v': 2}, place them into 3 labeled boxes with sizes [1, 3, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "Distribute the letters {'f': 2, 'u': 1, 'i': 3} among 3 identical containers that can hold [3, 2, 1] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH
[ { "content": "Distribute the letters {'p': 3, 'q': 1, 'o': 2} among 3 identical containers that can hold [2, 3, 1] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	12	MATH

[ { "content": "Distribute the letters {'v': 3, 'o': 1, 'y': 2} among 3 distinguishable boxes with capacities [2, 3, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "Given the letters {'c': 1, 'z': 1, 'x': 4}, place them into 3 labeled boxes with sizes [2, 1, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

8

MATH

[ { "content": "Arrange the letters {'q': 3, 'j': 2, 'l': 1} into 3 undistinguishable boxes with capacities [2, 2, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

3

MATH

[ { "content": "You have {'u': 2, 'w': 2, 'b': 2} and need to distribute them into 3 different boxes with capacities [2, 2, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

21

MATH

[ { "content": "Arrange the letters {'b': 2, 's': 3, 'c': 1} into 3 undistinguishable boxes with capacities [2, 2, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

3

MATH

[ { "content": "You have {'h': 1, 'a': 2, 'y': 3} and need to distribute them into 3 different boxes with capacities [2, 3, 1]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "Divide the letters from {'l': 2, 'u': 2, 'w': 2} into 3 undistinguishable boxes with sizes [2, 2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

5

MATH

[ { "content": "Distribute the letters {'i': 1, 'n': 1, 'o': 4} among 3 distinguishable boxes with capacities [3, 1, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

8

MATH

[ { "content": "Arrange the letters {'w': 1, 'v': 2, 'f': 3} into 3 undistinguishable boxes with capacities [1, 3, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "You have {'c': 2, 'a': 3, 'k': 1} and need to distribute them into 3 identical boxes with capacities [2, 2, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

3

MATH

[ { "content": "Given the letters {'w': 2, 'a': 3, 'g': 1}, place them into 3 labeled boxes with sizes [3, 1, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "You have {'z': 1, 'r': 3, 's': 2} and need to distribute them into 3 different boxes with capacities [1, 4, 1]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

8

MATH

[ { "content": "Arrange the letters {'i': 3, 'a': 1, 'j': 2} into 3 uniquely identified boxes that can hold [2, 2, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

15

MATH

[ { "content": "Given the letters {'o': 3, 'h': 2, 'c': 1}, place them into 3 labeled boxes with sizes [2, 2, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

15

MATH

[ { "content": "Arrange the letters {'t': 4, 'd': 1, 'e': 1} into 3 uniquely identified boxes that can hold [3, 1, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

8

MATH

[ { "content": "Distribute the letters {'h': 1, 'o': 2, 'v': 3} among 3 distinguishable boxes with capacities [1, 2, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "Distribute the letters {'h': 3, 'z': 1, 'a': 2} among 3 distinguishable boxes with capacities [2, 3, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "Given the letters {'t': 1, 'u': 1, 'd': 4}, place them into 3 labeled boxes with sizes [2, 2, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

9

MATH

[ { "content": "Divide the letters from {'d': 1, 'e': 3, 'b': 2} into 3 undistinguishable boxes with sizes [3, 1, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "Divide the letters from {'k': 2, 'd': 1, 'e': 3} into 3 undistinguishable boxes with sizes [3, 1, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "Distribute the letters {'v': 2, 't': 1, 'h': 3} among 3 identical containers that can hold [2, 1, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "Distribute the letters {'l': 3, 'h': 1, 'x': 2} among 3 distinguishable boxes with capacities [2, 2, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

15

MATH

[ { "content": "Given the letters {'k': 3, 'c': 2, 'q': 1}, place them into 3 indistinguishable boxes with sizes [3, 2, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "Distribute the letters {'h': 3, 'n': 2, 'c': 1} among 3 distinguishable boxes with capacities [2, 3, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "Arrange the letters {'d': 2, 'e': 1, 'j': 3} into 3 uniquely identified boxes that can hold [1, 2, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "Arrange the letters {'g': 4, 'b': 1, 'c': 1} into 3 undistinguishable boxes with capacities [2, 1, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

8

MATH

[ { "content": "Arrange the letters {'v': 1, 'x': 2, 'z': 3} into 3 uniquely identified boxes that can hold [1, 1, 4] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

8

MATH

[ { "content": "Divide the letters from {'q': 1, 't': 3, 'w': 2} into 3 undistinguishable boxes with sizes [4, 1, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

5

MATH

[ { "content": "Given the letters {'b': 2, 'a': 2, 'e': 2}, place them into 3 indistinguishable boxes with sizes [1, 2, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

15

MATH

[ { "content": "Distribute the letters {'o': 2, 'r': 2, 'm': 2} among 3 identical containers that can hold [2, 2, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

5

MATH

[ { "content": "Given the letters {'g': 2, 'i': 2, 'b': 2}, place them into 3 labeled boxes with sizes [3, 1, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

15

MATH

[ { "content": "Divide the letters from {'c': 3, 'j': 2, 'h': 1} into 3 distinctively labeled boxes with sizes [2, 1, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "You have {'s': 2, 'm': 3, 'g': 1} and need to distribute them into 3 different boxes with capacities [3, 1, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "Divide the letters from {'r': 2, 'f': 3, 'q': 1} into 3 undistinguishable boxes with sizes [1, 1, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

5

MATH

[ { "content": "Arrange the letters {'o': 2, 'f': 1, 'j': 3} into 3 undistinguishable boxes with capacities [1, 2, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "Divide the letters from {'y': 1, 'f': 1, 'c': 4} into 3 undistinguishable boxes with sizes [3, 1, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

8

MATH

[ { "content": "Arrange the letters {'q': 3, 'm': 2, 'o': 1} into 3 undistinguishable boxes with capacities [4, 1, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

5

MATH

[ { "content": "Given the letters {'i': 2, 'l': 1, 'v': 3}, place them into 3 indistinguishable boxes with sizes [3, 1, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "Divide the letters from {'p': 2, 'h': 2, 'z': 2} into 3 distinctively labeled boxes with sizes [2, 2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

21

MATH

[ { "content": "Distribute the letters {'r': 3, 't': 2, 'u': 1} among 3 identical containers that can hold [2, 2, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

3

MATH

[ { "content": "Given the letters {'e': 2, 'h': 2, 'c': 2}, place them into 3 indistinguishable boxes with sizes [2, 2, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

5

MATH

[ { "content": "Given the letters {'q': 3, 'g': 2, 'p': 1}, place them into 3 labeled boxes with sizes [1, 1, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

8

MATH

[ { "content": "Given the letters {'f': 1, 'q': 3, 'o': 2}, place them into 3 indistinguishable boxes with sizes [2, 2, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

3

MATH

[ { "content": "Given the letters {'o': 2, 'g': 1, 'j': 3}, place them into 3 labeled boxes with sizes [1, 2, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "Given the letters {'b': 1, 'v': 2, 'w': 3}, place them into 3 labeled boxes with sizes [1, 2, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "Given the letters {'l': 2, 'v': 2, 'd': 2}, place them into 3 indistinguishable boxes with sizes [3, 2, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

15

MATH

[ { "content": "Arrange the letters {'r': 1, 'o': 3, 'j': 2} into 3 uniquely identified boxes that can hold [3, 1, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "Distribute the letters {'c': 1, 'r': 2, 'm': 3} among 3 distinguishable boxes with capacities [2, 3, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "Given the letters {'f': 2, 'n': 1, 'l': 3}, place them into 3 labeled boxes with sizes [3, 1, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "You have {'v': 3, 'b': 2, 'o': 1} and need to distribute them into 3 identical boxes with capacities [3, 1, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "Distribute the letters {'k': 2, 's': 3, 'y': 1} among 3 distinguishable boxes with capacities [3, 1, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "You have {'e': 2, 'd': 3, 'v': 1} and need to distribute them into 3 identical boxes with capacities [2, 2, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

3

MATH

[ { "content": "Distribute the letters {'u': 3, 'y': 1, 'k': 2} among 3 identical containers that can hold [2, 2, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

3

MATH

[ { "content": "Divide the letters from {'s': 2, 'n': 2, 'p': 2} into 3 distinctively labeled boxes with sizes [2, 2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

21

MATH

[ { "content": "Arrange the letters {'w': 2, 'p': 1, 'f': 3} into 3 undistinguishable boxes with capacities [1, 2, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "Arrange the letters {'b': 2, 's': 1, 'k': 3} into 3 uniquely identified boxes that can hold [2, 1, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "Arrange the letters {'i': 1, 'z': 4, 'm': 1} into 3 undistinguishable boxes with capacities [1, 3, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

8

MATH

[ { "content": "Distribute the letters {'m': 3, 'l': 1, 'h': 2} among 3 distinguishable boxes with capacities [2, 2, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

15

MATH

[ { "content": "Divide the letters from {'j': 3, 'k': 2, 'r': 1} into 3 undistinguishable boxes with sizes [1, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "Divide the letters from {'i': 2, 'q': 1, 'o': 3} into 3 distinctively labeled boxes with sizes [1, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "Given the letters {'y': 1, 'h': 2, 'z': 3}, place them into 3 labeled boxes with sizes [1, 3, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "Given the letters {'e': 2, 'd': 1, 'u': 3}, place them into 3 labeled boxes with sizes [1, 4, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

8

MATH

[ { "content": "You have {'w': 2, 'q': 3, 'p': 1} and need to distribute them into 3 different boxes with capacities [1, 4, 1]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

8

MATH

[ { "content": "Distribute the letters {'h': 3, 'z': 1, 'j': 2} among 3 distinguishable boxes with capacities [3, 1, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "You have {'g': 2, 'j': 2, 'y': 2} and need to distribute them into 3 identical boxes with capacities [3, 2, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

15

MATH

[ { "content": "You have {'i': 1, 'n': 2, 'v': 3} and need to distribute them into 3 different boxes with capacities [2, 2, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

15

MATH

[ { "content": "Given the letters {'f': 2, 'k': 1, 'y': 3}, place them into 3 labeled boxes with sizes [2, 3, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "Distribute the letters {'d': 1, 'f': 3, 'h': 2} among 3 identical containers that can hold [1, 1, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

5

MATH

[ { "content": "Distribute the letters {'t': 3, 'g': 2, 'p': 1} among 3 identical containers that can hold [2, 2, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

3

MATH

[ { "content": "Divide the letters from {'y': 2, 'm': 2, 'c': 2} into 3 undistinguishable boxes with sizes [1, 4, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

6

MATH

[ { "content": "Arrange the letters {'z': 1, 'b': 2, 'x': 3} into 3 undistinguishable boxes with capacities [1, 3, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "Arrange the letters {'q': 2, 'b': 3, 'o': 1} into 3 uniquely identified boxes that can hold [2, 1, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "You have {'l': 2, 'b': 1, 'w': 3} and need to distribute them into 3 different boxes with capacities [1, 3, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "Distribute the letters {'h': 4, 'z': 1, 'b': 1} among 3 distinguishable boxes with capacities [1, 3, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

8

MATH

[ { "content": "Given the letters {'a': 4, 'h': 1, 'n': 1}, place them into 3 indistinguishable boxes with sizes [2, 2, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

2

MATH

[ { "content": "Given the letters {'j': 3, 'h': 1, 'w': 2}, place them into 3 indistinguishable boxes with sizes [2, 2, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

3

MATH

[ { "content": "Divide the letters from {'d': 3, 'l': 1, 'e': 2} into 3 undistinguishable boxes with sizes [4, 1, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

5

MATH

[ { "content": "You have {'f': 1, 'j': 2, 'v': 3} and need to distribute them into 3 different boxes with capacities [2, 2, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

15

MATH

[ { "content": "Given the letters {'g': 1, 'w': 2, 'y': 3}, place them into 3 indistinguishable boxes with sizes [1, 3, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "Divide the letters from {'g': 1, 'q': 2, 'y': 3} into 3 distinctively labeled boxes with sizes [2, 2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

15

MATH

[ { "content": "Divide the letters from {'t': 1, 'c': 3, 'q': 2} into 3 distinctively labeled boxes with sizes [1, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "Distribute the letters {'g': 2, 'e': 2, 'c': 2} among 3 distinguishable boxes with capacities [2, 1, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

15

MATH

[ { "content": "Distribute the letters {'a': 1, 'd': 3, 'g': 2} among 3 distinguishable boxes with capacities [1, 3, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "Divide the letters from {'d': 2, 'p': 1, 'r': 3} into 3 distinctively labeled boxes with sizes [1, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "Arrange the letters {'k': 2, 'g': 2, 'i': 2} into 3 undistinguishable boxes with capacities [2, 1, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

15

MATH

[ { "content": "Arrange the letters {'u': 1, 't': 1, 'r': 4} into 3 undistinguishable boxes with capacities [1, 4, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

4

MATH

[ { "content": "Arrange the letters {'l': 1, 'g': 2, 'u': 3} into 3 uniquely identified boxes that can hold [2, 1, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "You have {'y': 3, 'z': 2, 'i': 1} and need to distribute them into 3 identical boxes with capacities [1, 2, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "Given the letters {'k': 1, 'l': 3, 'e': 2}, place them into 3 indistinguishable boxes with sizes [1, 2, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "Divide the letters from {'l': 3, 'b': 1, 'c': 2} into 3 undistinguishable boxes with sizes [2, 1, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "Divide the letters from {'o': 2, 'x': 2, 'd': 2} into 3 undistinguishable boxes with sizes [1, 1, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

6

MATH

[ { "content": "Given the letters {'n': 2, 'h': 3, 'g': 1}, place them into 3 labeled boxes with sizes [2, 2, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

15

MATH

[ { "content": "Given the letters {'x': 2, 'n': 1, 's': 3}, place them into 3 indistinguishable boxes with sizes [2, 1, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "Arrange the letters {'a': 3, 'd': 2, 'x': 1} into 3 uniquely identified boxes that can hold [2, 2, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

15

MATH

[ { "content": "Given the letters {'f': 2, 'c': 2, 'y': 2}, place them into 3 labeled boxes with sizes [2, 3, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

15

MATH

[ { "content": "Given the letters {'f': 4, 'v': 1, 's': 1}, place them into 3 labeled boxes with sizes [1, 1, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "Given the letters {'x': 3, 'l': 1, 'j': 2}, place them into 3 indistinguishable boxes with sizes [3, 2, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "Given the letters {'o': 1, 'j': 3, 'v': 2}, place them into 3 labeled boxes with sizes [1, 3, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "Distribute the letters {'f': 2, 'u': 1, 'i': 3} among 3 identical containers that can hold [3, 2, 1] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH

[ { "content": "Distribute the letters {'p': 3, 'q': 1, 'o': 2} among 3 identical containers that can hold [2, 3, 1] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

12

MATH