messages listlengths 1 1 | ground_truth stringclasses 115 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Divide the letters from {'q': 4, 'e': 3, 's': 2} into 4 distinctively labeled boxes with sizes [3, 2, 3, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 87 | MATH |
[
{
"content": "Given the letters {'h': 1, 'q': 4, 'z': 2, 'd': 2}, place them into 4 indistinguishable boxes with sizes [1, 5, 2, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 58 | MATH |
[
{
"content": "You have {'n': 1, 'x': 2, 'g': 3} and need to distribute them into 4 different boxes with capacities [2, 1, 2, 1]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "Arrange the letters {'i': 1, 'v': 2, 's': 2, 'x': 1} 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"
}
] | 17 | MATH |
[
{
"content": "You have {'m': 1, 'k': 2, 'w': 2, 'a': 3} 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 {'s': 3, 'd': 2, 'b': 5} into 4 distinctively labeled boxes with sizes [3, 2, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 130 | MATH |
[
{
"content": "You have {'v': 1, 'f': 1, 'x': 4} 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"
}
] | 8 | MATH |
[
{
"content": "Divide the letters from {'u': 3, 'v': 2, 'q': 3} into 3 undistinguishable boxes with sizes [2, 2, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "You have {'j': 1, 'e': 2, 'y': 3, 'q': 1} and need to distribute them into 3 identical boxes with capacities [2, 3, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Given the letters {'j': 1, 'z': 1, 'u': 3, 'r': 1}, place them into 4 labeled boxes with sizes [1, 1, 2, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 42 | MATH |
[
{
"content": "Distribute the letters {'p': 1, 'd': 2, 'o': 3} among 4 identical containers that can hold [1, 2, 1, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Divide the letters from {'v': 2, 'u': 2, 'd': 2, 'm': 2} into 3 distinctively labeled boxes with sizes [3, 3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 88 | MATH |
[
{
"content": "You have {'m': 2, 'o': 3, 'a': 5} and need to distribute them into 3 different boxes with capacities [2, 3, 5]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Distribute the letters {'m': 2, 'c': 4, 'w': 1} 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"
}
] | 25 | MATH |
[
{
"content": "You have {'j': 2, 'h': 3, 'd': 2} and need to distribute them into 4 different boxes with capacities [2, 2, 1, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 51 | MATH |
[
{
"content": "Arrange the letters {'t': 1, 'e': 1, 'o': 3, 'a': 1} into 4 undistinguishable boxes with capacities [2, 2, 1, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "Distribute the letters {'x': 2, 'd': 5, 's': 3} among 3 distinguishable boxes with capacities [3, 3, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 49 | MATH |
[
{
"content": "Arrange the letters {'j': 2, 'o': 1, 's': 3} 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": "You have {'z': 1, 's': 2, 'u': 2, 'o': 1} and need to distribute them into 4 different boxes with capacities [2, 1, 2, 1]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 58 | MATH |
[
{
"content": "Given the letters {'w': 3, 'i': 3, 'u': 2}, place them into 3 indistinguishable boxes with sizes [3, 3, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18 | MATH |
[
{
"content": "Arrange the letters {'v': 2, 'h': 1, 'w': 2, 'x': 2} into 4 undistinguishable boxes with capacities [2, 3, 1, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 51 | MATH |
[
{
"content": "Divide the letters from {'p': 5, 'f': 2, 'h': 2, 'i': 1} into 3 undistinguishable boxes with sizes [5, 3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 76 | MATH |
[
{
"content": "Given the letters {'s': 3, 'g': 5, 'a': 1}, place them into 3 indistinguishable boxes with sizes [6, 2, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13 | MATH |
[
{
"content": "Distribute the letters {'h': 4, 'u': 2, 'r': 1, 'f': 3} among 4 distinguishable boxes with capacities [2, 4, 2, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 334 | MATH |
[
{
"content": "You have {'v': 3, 'd': 3, 'l': 2, 'o': 1} and need to distribute them into 4 different boxes with capacities [1, 3, 1, 4]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 145 | MATH |
[
{
"content": "Given the letters {'k': 1, 'b': 4, 'o': 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": "Distribute the letters {'l': 2, 's': 1, 'c': 3} among 4 identical containers that can hold [1, 1, 2, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Divide the letters from {'o': 3, 'l': 3, 'a': 3} into 4 distinctively labeled boxes with sizes [2, 4, 2, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 87 | MATH |
[
{
"content": "You have {'h': 2, 't': 1, 'r': 2, 'x': 4} and need to distribute them into 4 different boxes with capacities [3, 3, 1, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 188 | MATH |
[
{
"content": "Distribute the letters {'y': 2, 'r': 3, 'q': 3, 't': 2} 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": "You have {'a': 1, 'f': 1, 'd': 4, 'n': 3} and need to distribute them into 4 different boxes with capacities [3, 1, 1, 4]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 101 | MATH |
[
{
"content": "You have {'w': 3, 'd': 1, 'l': 1, 'c': 2} and need to distribute them into 4 identical boxes with capacities [1, 2, 1, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 39 | MATH |
[
{
"content": "Given the letters {'m': 2, 'l': 3, 'e': 2, 'c': 1}, place them into 4 labeled boxes with sizes [2, 1, 2, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 154 | MATH |
[
{
"content": "Distribute the letters {'t': 1, 'd': 3, 'n': 3} among 3 identical containers that can hold [2, 4, 1] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13 | MATH |
[
{
"content": "Given the letters {'j': 3, 's': 1, 'k': 2, 'y': 1}, place them into 3 labeled boxes with sizes [2, 4, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | MATH |
[
{
"content": "Divide the letters from {'r': 1, 'l': 1, 'x': 2, 'q': 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"
}
] | 24 | MATH |
[
{
"content": "You have {'w': 3, 'u': 1, 'j': 3} and need to distribute them into 4 different boxes with capacities [2, 2, 2, 1]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 37 | MATH |
[
{
"content": "Distribute the letters {'j': 3, 'n': 4, 'l': 1, 'i': 2} among 4 identical containers that can hold [2, 3, 1, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 261 | MATH |
[
{
"content": "Distribute the letters {'u': 2, 'j': 1, 'b': 3, 's': 2} among 4 distinguishable boxes with capacities [2, 2, 1, 3]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 154 | MATH |
[
{
"content": "Arrange the letters {'b': 2, 'e': 1, 't': 2, 'u': 1} into 3 undistinguishable boxes with capacities [2, 3, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "Divide the letters from {'o': 4, 'j': 3, 'l': 3} into 4 undistinguishable boxes with sizes [3, 2, 4, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 123 | MATH |
[
{
"content": "Arrange the letters {'y': 2, 'q': 3, 'o': 2, 'i': 3} into 3 undistinguishable boxes with capacities [3, 3, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 92 | MATH |
[
{
"content": "Divide the letters from {'a': 2, 'w': 4, 's': 1, 'd': 2} into 3 undistinguishable boxes with sizes [4, 1, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | MATH |
[
{
"content": "Divide the letters from {'c': 3, 'w': 1, 'x': 3} into 4 undistinguishable boxes with sizes [1, 3, 1, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "Given the letters {'b': 3, 'n': 1, 't': 3}, place them into 3 labeled boxes with sizes [3, 3, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "Arrange the letters {'t': 3, 'x': 3, 'v': 2} into 3 undistinguishable boxes with capacities [3, 1, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 23 | MATH |
[
{
"content": "Given the letters {'u': 2, 's': 3, 'n': 1, 'a': 1}, place them into 3 labeled boxes with sizes [4, 2, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | MATH |
[
{
"content": "Divide the letters from {'p': 3, 'c': 2, 'b': 1} into 3 undistinguishable boxes with sizes [1, 3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "Arrange the letters {'z': 1, 'h': 2, 'c': 1, 'p': 2} into 3 undistinguishable boxes with capacities [2, 3, 1]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "Given the letters {'e': 4, 'r': 3, 'h': 2}, place them into 3 labeled boxes with sizes [1, 4, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 27 | MATH |
[
{
"content": "Arrange the letters {'r': 3, 'v': 4, 'y': 2} into 3 undistinguishable boxes with capacities [4, 2, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 39 | MATH |
[
{
"content": "Distribute the letters {'a': 1, 't': 4, 'q': 1} among 4 distinguishable boxes with capacities [1, 3, 1, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13 | MATH |
[
{
"content": "Given the letters {'k': 1, 'b': 2, 'y': 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": "Arrange the letters {'f': 2, 'r': 3, 'u': 1} into 4 uniquely identified boxes that can hold [1, 1, 3, 1] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "You have {'j': 2, 'n': 2, 'r': 2} and need to distribute them into 4 different boxes with capacities [1, 2, 2, 1]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 33 | MATH |
[
{
"content": "Arrange the letters {'h': 4, 'a': 2, 'w': 1} into 3 undistinguishable boxes with capacities [1, 1, 5]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "You have {'u': 1, 'e': 2, 'n': 2, 'j': 2} and need to distribute them into 3 identical boxes with capacities [1, 3, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "Distribute the letters {'d': 1, 'u': 1, 'y': 2, 'c': 3} 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 {'b': 3, 'q': 5, 'n': 2} among 4 identical containers that can hold [2, 3, 3, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 39 | MATH |
[
{
"content": "Arrange the letters {'y': 1, 'q': 3, 'w': 1, 'k': 1} 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"
}
] | 19 | MATH |
[
{
"content": "Distribute the letters {'u': 2, 'o': 2, 'c': 3} among 3 identical containers that can hold [1, 5, 1] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "You have {'h': 1, 'o': 2, 'i': 2, 't': 2} and need to distribute them into 4 identical boxes with capacities [1, 1, 2, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 51 | MATH |
[
{
"content": "You have {'m': 2, 'v': 2, 'j': 4} and need to distribute them into 3 identical boxes with capacities [5, 2, 1]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "Arrange the letters {'z': 3, 'a': 3, 'c': 4} 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"
}
] | 49 | MATH |
[
{
"content": "Divide the letters from {'w': 4, 'z': 1, 'e': 3, 'n': 2} into 3 distinctively labeled boxes with sizes [6, 3, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 50 | MATH |
[
{
"content": "Arrange the letters {'b': 3, 'l': 2, 'i': 4} into 3 uniquely identified boxes that can hold [5, 2, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "You have {'g': 1, 'u': 4, 'x': 4} and need to distribute them into 3 identical boxes with capacities [4, 3, 2]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 27 | MATH |
[
{
"content": "You have {'c': 1, 's': 1, 'z': 2, 'n': 2} and need to distribute them into 3 different boxes with capacities [1, 2, 3]. 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 {'x': 2, 'r': 3, 'a': 2} and need to distribute them into 3 different boxes with capacities [3, 3, 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 {'l': 5, 'p': 1, 'i': 3}, place them into 3 indistinguishable boxes with sizes [2, 4, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "Arrange the letters {'i': 2, 'y': 1, 'k': 2, 'z': 2} into 3 undistinguishable boxes with capacities [2, 3, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 27 | MATH |
[
{
"content": "Distribute the letters {'m': 4, 's': 4, 'f': 1} among 4 distinguishable boxes with capacities [3, 1, 3, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 56 | MATH |
[
{
"content": "Distribute the letters {'r': 3, 'b': 3, 'v': 3} among 4 distinguishable boxes with capacities [1, 2, 2, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 87 | MATH |
[
{
"content": "Divide the letters from {'c': 2, 'f': 3, 'r': 2, 'o': 2} into 4 distinctively labeled boxes with sizes [3, 1, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 295 | MATH |
[
{
"content": "Divide the letters from {'v': 3, 'f': 2, 't': 2, 'c': 2} into 4 undistinguishable boxes with sizes [3, 2, 2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 78 | MATH |
[
{
"content": "Distribute the letters {'i': 1, 't': 3, 'm': 2} among 4 distinguishable boxes with capacities [2, 2, 1, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "Divide the letters from {'m': 2, 'r': 4, 'k': 2} 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"
}
] | 29 | MATH |
[
{
"content": "Distribute the letters {'t': 1, 'y': 3, 'u': 5} among 4 distinguishable boxes with capacities [2, 1, 4, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 44 | MATH |
[
{
"content": "Distribute the letters {'i': 1, 'p': 2, 'j': 3, 'v': 1} among 4 identical containers that can hold [2, 1, 1, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 39 | MATH |
[
{
"content": "Given the letters {'x': 1, 'j': 4, 'a': 1, 'c': 1}, place them into 3 indistinguishable boxes with sizes [1, 4, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "Given the letters {'w': 2, 's': 2, 'b': 2, 'a': 2}, place them into 4 indistinguishable boxes with sizes [2, 2, 3, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 108 | MATH |
[
{
"content": "You have {'n': 2, 'q': 1, 'x': 3, 'b': 2} and need to distribute them into 3 identical boxes with capacities [1, 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 {'z': 4, 'v': 2, 's': 2, 'n': 2} into 3 uniquely identified boxes that can hold [1, 6, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 59 | MATH |
[
{
"content": "Arrange the letters {'b': 1, 'q': 1, 't': 2, 'c': 3} into 4 undistinguishable boxes with capacities [1, 2, 2, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "Given the letters {'i': 3, 'j': 1, 'm': 2, 'v': 2}, place them into 3 labeled boxes with sizes [4, 3, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 43 | MATH |
[
{
"content": "Distribute the letters {'a': 3, 'y': 2, 'w': 3} among 3 identical containers that can hold [1, 2, 5] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17 | MATH |
[
{
"content": "Given the letters {'v': 1, 'b': 1, 'h': 4, 'y': 2}, place them into 3 indistinguishable boxes with sizes [4, 3, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31 | MATH |
[
{
"content": "Divide the letters from {'n': 2, 'e': 1, 'q': 1, 'w': 2} into 4 distinctively labeled boxes with sizes [1, 2, 2, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 58 | MATH |
[
{
"content": "Distribute the letters {'w': 3, 'x': 1, 'd': 2, 'r': 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": "Divide the letters from {'y': 2, 'g': 2, 'r': 3, 'z': 1} into 3 undistinguishable boxes with sizes [2, 5, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31 | MATH |
[
{
"content": "Divide the letters from {'l': 3, 'o': 2, 'e': 1, 'v': 1} into 3 undistinguishable boxes with sizes [1, 2, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | MATH |
[
{
"content": "Given the letters {'v': 4, 'g': 3, 'i': 2}, place them into 4 indistinguishable boxes with sizes [1, 2, 2, 4]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 42 | MATH |
[
{
"content": "Divide the letters from {'z': 2, 'w': 2, 't': 2, 'g': 1} into 3 distinctively labeled boxes with sizes [3, 3, 1]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 37 | MATH |
[
{
"content": "Arrange the letters {'k': 4, 't': 2, 'y': 2, 'd': 1} into 4 uniquely identified boxes that can hold [1, 2, 3, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 188 | MATH |
[
{
"content": "Distribute the letters {'e': 2, 'b': 2, 'a': 4, 'h': 2} among 4 identical containers that can hold [3, 4, 2, 1] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 334 | MATH |
[
{
"content": "Distribute the letters {'o': 3, 'e': 2, 'r': 3, 'c': 2} among 4 identical containers that can hold [4, 3, 1, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 392 | MATH |
[
{
"content": "Given the letters {'g': 4, 'e': 1, 'b': 3, 'z': 1}, place them into 4 labeled boxes with sizes [2, 3, 2, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 181 | MATH |
[
{
"content": "Arrange the letters {'q': 5, 'c': 1, 'r': 3} into 4 undistinguishable boxes with capacities [1, 1, 2, 5]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Given the letters {'q': 1, 'g': 2, 'b': 3}, place them into 4 labeled boxes with sizes [2, 1, 2, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "Given the letters {'z': 1, 'b': 1, 's': 2, 'n': 2}, place them into 3 labeled boxes with sizes [3, 2, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
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