messages
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1
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[ { "content": "Given the letters {'g': 4, 't': 2, 'y': 1}, place them into 4 indistinguishable boxes with sizes [2, 2, 2, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
7
MATH
[ { "content": "Divide the letters from {'p': 2, 'v': 2, 'l': 1, 'b': 1} into 3 distinctively labeled boxes with sizes [2, 3, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
24
MATH
[ { "content": "Divide the letters from {'m': 3, 'q': 1, 'x': 4} into 3 distinctively labeled boxes with sizes [2, 3, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
23
MATH
[ { "content": "Divide the letters from {'l': 3, 'y': 2, 'k': 1, 'e': 2} into 4 distinctively labeled boxes with sizes [2, 2, 2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
204
MATH
[ { "content": "You have {'f': 2, 'i': 1, 'j': 5, 'g': 1} and need to distribute them into 4 identical boxes with capacities [1, 3, 3, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
54
MATH
[ { "content": "Arrange the letters {'t': 2, 'h': 3, 'r': 1} into 4 uniquely identified boxes that can hold [2, 1, 1, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
24
MATH
[ { "content": "You have {'j': 2, 'f': 3, 'm': 2} and need to distribute them into 4 different boxes with capacities [1, 2, 2, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
51
MATH
[ { "content": "Distribute the letters {'a': 1, 'd': 3, 'j': 4} among 3 identical containers that can hold [3, 2, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
12
MATH
[ { "content": "Arrange the letters {'u': 4, 'z': 1, 'o': 2, 's': 3} into 4 uniquely identified boxes that can hold [2, 2, 3, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
392
MATH
[ { "content": "You have {'p': 2, 'q': 4, 'v': 1, 'i': 3} and need to distribute them into 4 different boxes with capacities [4, 4, 1, 1]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
174
MATH
[ { "content": "Distribute the letters {'o': 1, 'a': 3, 'w': 2, 'e': 1} among 4 identical containers that can hold [2, 2, 2, 1] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
16
MATH
[ { "content": "Distribute the letters {'c': 1, 'l': 2, 'd': 1, 't': 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" } ]
24
MATH
[ { "content": "You have {'n': 2, 'h': 3, 'c': 1} and need to distribute them into 4 different boxes with capacities [1, 2, 1, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
24
MATH
[ { "content": "You have {'f': 2, 'd': 2, 'o': 4, 'l': 1} and need to distribute them into 3 identical boxes with capacities [2, 2, 5]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
31
MATH
[ { "content": "Arrange the letters {'h': 1, 'z': 3, 's': 2} into 4 undistinguishable boxes with capacities [1, 1, 2, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
8
MATH
[ { "content": "Given the letters {'a': 2, 'c': 2, 'k': 1, 'n': 2}, place them into 4 labeled boxes with sizes [2, 2, 1, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
120
MATH
[ { "content": "Divide the letters from {'r': 2, 'f': 2, 'x': 3} into 4 undistinguishable boxes with sizes [3, 2, 1, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
25
MATH
[ { "content": "Distribute the letters {'q': 2, 'n': 1, 'u': 2, 's': 3} among 4 distinguishable boxes with capacities [2, 3, 2, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
154
MATH
[ { "content": "Divide the letters from {'p': 5, 'j': 1, 't': 2, 'a': 1} into 4 undistinguishable boxes with sizes [2, 4, 2, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
52
MATH
[ { "content": "You have {'n': 3, 'h': 1, 'b': 2} and need to distribute them into 4 different boxes with capacities [3, 1, 1, 1]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
19
MATH
[ { "content": "Given the letters {'n': 4, 'e': 1, 'w': 3}, place them into 3 indistinguishable boxes with sizes [2, 2, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
11
MATH
[ { "content": "Arrange the letters {'o': 3, 'c': 2, 'n': 3} into 3 undistinguishable boxes with capacities [5, 2, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
17
MATH
[ { "content": "Distribute the letters {'v': 4, 's': 3, 'd': 2} among 3 identical containers that can hold [2, 3, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
39
MATH
[ { "content": "You have {'j': 3, 'w': 2, 'c': 1} and need to distribute them into 3 identical boxes with capacities [2, 1, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
12
MATH
[ { "content": "You have {'f': 1, 't': 2, 'a': 4} and need to distribute them into 3 identical boxes with capacities [2, 4, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
12
MATH
[ { "content": "Arrange the letters {'e': 3, 'q': 3, 'f': 2, 'p': 2} into 4 uniquely identified boxes that can hold [4, 1, 3, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
392
MATH
[ { "content": "Divide the letters from {'h': 4, 'n': 3, 'q': 2} into 3 distinctively labeled boxes with sizes [1, 6, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
17
MATH
[ { "content": "You have {'n': 2, 'd': 3, 'j': 2} and need to distribute them into 3 different boxes with capacities [2, 3, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
25
MATH
[ { "content": "Given the letters {'i': 3, 'c': 3, 'k': 3, 'q': 1}, place them into 3 labeled boxes with sizes [4, 2, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
120
MATH
[ { "content": "Given the letters {'c': 2, 's': 3, 't': 2, 'p': 3}, place them into 3 indistinguishable boxes with sizes [4, 4, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
75
MATH
[ { "content": "Given the letters {'i': 1, 'p': 2, 'j': 2, 'z': 1}, place them into 4 indistinguishable boxes with sizes [2, 1, 2, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
17
MATH
[ { "content": "Arrange the letters {'x': 4, 'j': 4, 'y': 1, 'f': 1} into 3 undistinguishable boxes with capacities [2, 2, 6]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
25
MATH
[ { "content": "Distribute the letters {'q': 5, 'e': 3, 'r': 2} among 3 identical containers that can hold [3, 3, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
26
MATH
[ { "content": "Divide the letters from {'o': 3, 'e': 4, 'p': 1} into 4 distinctively labeled boxes with sizes [2, 2, 2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
52
MATH
[ { "content": "Given the letters {'f': 1, 'r': 5, 'x': 4}, place them into 4 labeled boxes with sizes [2, 6, 1, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
32
MATH
[ { "content": "Divide the letters from {'m': 1, 'o': 2, 'l': 1, 'r': 2} into 3 undistinguishable boxes with sizes [3, 2, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
24
MATH
[ { "content": "Distribute the letters {'j': 2, 't': 3, 'a': 1, 'q': 1} among 3 distinguishable boxes with capacities [2, 3, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
39
MATH
[ { "content": "Given the letters {'a': 2, 'i': 2, 'f': 4}, place them into 3 indistinguishable boxes with sizes [2, 3, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
16
MATH
[ { "content": "You have {'q': 3, 'n': 2, 'e': 5} and need to distribute them into 4 identical boxes with capacities [2, 4, 3, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
93
MATH
[ { "content": "Divide the letters from {'h': 2, 'z': 1, 'l': 3} 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": "Arrange the letters {'p': 3, 'g': 4, 'i': 3} into 3 undistinguishable boxes with capacities [2, 5, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
49
MATH
[ { "content": "Arrange the letters {'k': 4, 's': 2, 'r': 1} into 4 uniquely identified boxes that can hold [1, 2, 3, 1] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
25
MATH
[ { "content": "You have {'b': 3, 'g': 1, 'm': 1, 'c': 3} and need to distribute them into 4 different boxes with capacities [3, 3, 1, 1]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
92
MATH
[ { "content": "Given the letters {'d': 3, 'l': 2, 'f': 1, 'i': 4}, place them into 3 indistinguishable boxes with sizes [4, 4, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
53
MATH
[ { "content": "Distribute the letters {'t': 2, 'm': 1, 's': 3, 'i': 1} among 3 distinguishable boxes with capacities [2, 1, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
25
MATH
[ { "content": "Divide the letters from {'e': 2, 'o': 2, 'l': 1, 'w': 1} into 4 undistinguishable boxes with sizes [1, 1, 1, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
10
MATH
[ { "content": "Distribute the letters {'z': 2, 'n': 2, 'g': 2} among 4 identical containers that can hold [1, 1, 3, 1] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
7
MATH
[ { "content": "Arrange the letters {'e': 3, 'n': 3, 'o': 2, 'x': 2} into 4 uniquely identified boxes that can hold [1, 4, 1, 4] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
246
MATH
[ { "content": "Distribute the letters {'q': 3, 'c': 3, 'i': 3} among 3 identical containers that can hold [2, 3, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
45
MATH
[ { "content": "You have {'h': 2, 'b': 3, 'p': 1, 'o': 2} and need to distribute them into 3 identical boxes with capacities [4, 2, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
30
MATH
[ { "content": "Divide the letters from {'j': 2, 't': 2, 'a': 4} into 4 distinctively labeled boxes with sizes [2, 1, 3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
57
MATH
[ { "content": "Arrange the letters {'b': 6, 'k': 3, 'j': 1} into 3 uniquely identified boxes that can hold [5, 3, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
24
MATH
[ { "content": "Divide the letters from {'w': 1, 'l': 4, 'o': 1} into 4 undistinguishable boxes with sizes [1, 1, 3, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
4
MATH
[ { "content": "Distribute the letters {'b': 1, 'a': 2, 'h': 2, 'm': 2} among 4 identical containers that can hold [3, 1, 2, 1] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
51
MATH
[ { "content": "Given the letters {'o': 4, 'm': 1, 'x': 1}, 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" } ]
8
MATH
[ { "content": "Distribute the letters {'i': 1, 'e': 1, 'y': 5} among 3 distinguishable boxes with capacities [4, 1, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
8
MATH
[ { "content": "Given the letters {'c': 4, 'm': 2, 'y': 2}, place them into 3 indistinguishable boxes with sizes [2, 4, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
15
MATH
[ { "content": "Divide the letters from {'g': 2, 'p': 1, 'b': 3, 'z': 2} into 4 undistinguishable boxes with sizes [2, 2, 2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
11
MATH
[ { "content": "Distribute the letters {'l': 2, 'z': 3, 'b': 2, 'u': 1} among 3 distinguishable boxes with capacities [1, 4, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
43
MATH
[ { "content": "Divide the letters from {'p': 2, 'z': 4, 'a': 2, 'u': 2} into 3 distinctively labeled boxes with sizes [3, 3, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
153
MATH
[ { "content": "You have {'e': 4, 'n': 3, 'g': 2} and need to distribute them into 4 different boxes with capacities [4, 2, 1, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
75
MATH
[ { "content": "Arrange the letters {'t': 2, 'b': 3, 'g': 1} into 3 uniquely identified boxes that can hold [3, 2, 1] 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 {'g': 3, 'd': 2, 'z': 1, 'j': 2} among 3 distinguishable boxes with capacities [3, 3, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
69
MATH
[ { "content": "Distribute the letters {'z': 1, 'o': 1, 'c': 1, 'v': 3} among 4 identical containers that can hold [1, 2, 2, 1] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
12
MATH
[ { "content": "Given the letters {'n': 1, 'a': 2, 'g': 6, 'b': 1}, place them into 4 indistinguishable boxes with sizes [2, 2, 3, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
40
MATH
[ { "content": "Given the letters {'o': 1, 't': 5, 's': 3, 'q': 1}, place them into 4 indistinguishable boxes with sizes [4, 1, 3, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
154
MATH
[ { "content": "Distribute the letters {'b': 1, 'x': 3, 'r': 1, 'i': 1} among 4 distinguishable boxes with capacities [1, 2, 2, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
42
MATH
[ { "content": "Arrange the letters {'k': 2, 'g': 1, 't': 2, 'x': 1} into 4 uniquely identified boxes that can hold [2, 2, 1, 1] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
58
MATH
[ { "content": "Arrange the letters {'b': 4, 'c': 2, 'q': 2} into 4 undistinguishable boxes with capacities [2, 2, 3, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
32
MATH
[ { "content": "Arrange the letters {'g': 4, 'e': 2, 'i': 1} into 4 uniquely identified boxes that can hold [2, 1, 3, 1] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
25
MATH
[ { "content": "Distribute the letters {'z': 1, 'b': 2, 'g': 4} among 3 distinguishable boxes with capacities [2, 3, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
16
MATH
[ { "content": "Distribute the letters {'v': 1, 'd': 3, 'f': 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 {'m': 1, 'j': 2, 'f': 1, 'g': 2} among 4 distinguishable boxes with capacities [1, 2, 2, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
58
MATH
[ { "content": "Arrange the letters {'t': 4, 'n': 2, 'f': 4} into 4 uniquely identified boxes that can hold [2, 2, 2, 4] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
130
MATH
[ { "content": "Given the letters {'u': 2, 't': 2, 'l': 4}, place them into 4 labeled boxes with sizes [1, 2, 2, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
57
MATH
[ { "content": "Distribute the letters {'m': 3, 'a': 2, 'n': 2, 'g': 3} among 3 distinguishable boxes with capacities [3, 2, 5]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
130
MATH
[ { "content": "Distribute the letters {'t': 2, 'n': 2, 'c': 2, 'w': 4} among 3 distinguishable boxes with capacities [4, 3, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
153
MATH
[ { "content": "Given the letters {'c': 4, 'n': 3, 'p': 2}, place them into 4 labeled boxes with sizes [1, 3, 2, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
87
MATH
[ { "content": "Given the letters {'w': 1, 'z': 2, 'y': 1, 'u': 2}, place them into 4 indistinguishable boxes with sizes [2, 1, 2, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
17
MATH
[ { "content": "Given the letters {'p': 3, 'v': 2, 'j': 2, 'i': 3}, place them into 4 indistinguishable boxes with sizes [4, 1, 4, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
75
MATH
[ { "content": "Divide the letters from {'l': 1, 'y': 2, 'd': 1, 'h': 2} into 3 distinctively labeled boxes with sizes [2, 3, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
24
MATH
[ { "content": "Arrange the letters {'h': 1, 'x': 2, 'w': 2, 'j': 1} into 3 undistinguishable boxes with capacities [3, 2, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
24
MATH
[ { "content": "You have {'k': 3, 'q': 2, 'i': 3, 'o': 2} and need to distribute them into 4 different boxes with capacities [1, 4, 3, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
392
MATH
[ { "content": "Distribute the letters {'c': 2, 'n': 2, 'v': 3, 'z': 3} among 4 identical containers that can hold [2, 2, 4, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
102
MATH
[ { "content": "Arrange the letters {'x': 2, 'e': 1, 'w': 3} 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": "Given the letters {'i': 1, 'q': 1, 'j': 3, 'w': 1}, 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" } ]
19
MATH
[ { "content": "Arrange the letters {'y': 5, 'b': 1, 'p': 2} into 4 uniquely identified boxes that can hold [2, 3, 2, 1] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
31
MATH
[ { "content": "Given the letters {'f': 3, 'v': 4, 't': 2}, place them into 4 labeled boxes with sizes [3, 2, 2, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
109
MATH
[ { "content": "Arrange the letters {'s': 3, 'd': 2, 'j': 3, 'g': 2} into 4 uniquely identified boxes that can hold [2, 2, 4, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
517
MATH
[ { "content": "Divide the letters from {'h': 3, 's': 3, 'l': 4} into 3 distinctively labeled boxes with sizes [3, 5, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
49
MATH
[ { "content": "Divide the letters from {'e': 3, 'a': 2, 'c': 1, 'x': 2} into 3 distinctively labeled boxes with sizes [4, 2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
57
MATH
[ { "content": "You have {'r': 1, 'x': 4, 'p': 1} and need to distribute them into 4 identical boxes with capacities [2, 2, 1, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
5
MATH
[ { "content": "Given the letters {'t': 3, 'm': 1, 'l': 4}, place them into 4 indistinguishable boxes with sizes [2, 3, 1, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
24
MATH
[ { "content": "You have {'e': 4, 'h': 4, 'x': 1} and need to distribute them into 3 different boxes with capacities [2, 5, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
21
MATH
[ { "content": "Given the letters {'i': 3, 'z': 1, 'p': 1, 'y': 2}, place them into 3 indistinguishable boxes with sizes [3, 2, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
20
MATH
[ { "content": "Divide the letters from {'v': 3, 'f': 1, 'x': 2, 'n': 3} into 3 distinctively labeled boxes with sizes [2, 4, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
87
MATH
[ { "content": "Distribute the letters {'u': 1, 's': 2, 'v': 2, 'j': 2} among 4 distinguishable boxes with capacities [1, 3, 1, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
87
MATH
[ { "content": "Arrange the letters {'w': 1, 'a': 2, 'j': 6} into 4 uniquely identified boxes that can hold [2, 3, 1, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
32
MATH
[ { "content": "Given the letters {'j': 2, 'm': 4, 'y': 1, 'a': 1}, place them into 3 indistinguishable boxes with sizes [2, 3, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
23
MATH
[ { "content": "Given the letters {'i': 2, 'a': 2, 'g': 2, 's': 1}, place them into 3 labeled boxes with sizes [1, 3, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
37
MATH