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["combinatory_distribution_level_6_0000","combinatory_distribution",6,[{"content":"Distribute the letters {'d': 1, 'x': 3, 'q': 4, 'y': 2, 't': 3} among 5 distinguishable boxes with capacities [3, 3, 3, 2, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}","role":"user"}],"20959","MATH_PROB_FAMILIES"]
["combinatory_distribution_level_6_0001","combinatory_distribution",6,[{"content":"You have {'u': 3, 'p': 3, 'k': 2, 'd': 3, 'z': 2} and need to distribute them into 5 identical boxes with capacities [2, 2, 3, 2, 4]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}","role":"user"}],"5235","MATH_PROB_FAMILIES"]
["combinatory_distribution_level_6_0002","combinatory_distribution",6,[{"content":"Divide the letters from {'o': 1, 'r': 3, 'w': 3, 'c': 2, 'q': 4} into 5 undistinguishable boxes with sizes [3, 4, 2, 2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}","role":"user"}],"3290","MATH_PROB_FAMILIES"]
["combinatory_distribution_level_6_0003","combinatory_distribution",6,[{"content":"Divide the letters from {'b': 2, 'n': 2, 'e': 3, 'k': 2, 's': 4} into 5 undistinguishable boxes with sizes [4, 1, 2, 2, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}","role":"user"}],"3791","MATH_PROB_FAMILIES"]
["combinatory_distribution_level_6_0004","combinatory_distribution",6,[{"content":"Arrange the letters {'p': 2, 's': 3, 'x': 3, 'j': 3, 'r': 2} into 5 uniquely identified boxes that can hold [2, 1, 4, 4, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}","role":"user"}],"17160","MATH_PROB_FAMILIES"]
["combinatory_distribution_level_6_0005","combinatory_distribution",6,[{"content":"You have {'b': 4, 'r': 1, 'j': 2, 'z': 3, 'x': 3} and need to distribute them into 5 different boxes with capacities [3, 1, 2, 5, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}","role":"user"}],"9609","MATH_PROB_FAMILIES"]
["combinatory_distribution_level_6_0006","combinatory_distribution",6,[{"content":"Given the letters {'f': 1, 'd': 6, 'y': 2, 'u': 2, 'a': 2}, place them into 5 labeled boxes with sizes [2, 2, 4, 3, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}","role":"user"}],"8158","MATH_PROB_FAMILIES"]
["combinatory_distribution_level_6_0007","combinatory_distribution",6,[{"content":"You have {'x': 2, 'g': 3, 'r': 4, 'j': 2, 'h': 3} and need to distribute them into 5 identical boxes with capacities [5, 3, 3, 2, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}","role":"user"}],"13113","MATH_PROB_FAMILIES"]
["combinatory_distribution_level_6_0008","combinatory_distribution",6,[{"content":"Arrange the letters {'o': 6, 'l': 1, 'd': 2, 'y': 2, 'v': 3} into 5 undistinguishable boxes with capacities [2, 2, 2, 5, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}","role":"user"}],"2568","MATH_PROB_FAMILIES"]
["combinatory_distribution_level_6_0009","combinatory_distribution",6,[{"content":"Arrange the letters {'w': 3, 'c': 3, 'n': 3, 'q': 3, 'r': 2} into 5 undistinguishable boxes with capacities [2, 5, 2, 3, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}","role":"user"}],"7644","MATH_PROB_FAMILIES"]