messages listlengths 1 1 | ground_truth stringclasses 115
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Distribute the letters {'s': 3, 'p': 6} among 2 identical containers that can hold [5, 4] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Arrange the letters {'w': 4, 'n': 3} into 3 undistinguishable boxes with capacities [3, 2, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "Arrange the letters {'d': 3, 'a': 3} into 3 uniquely identified boxes that can hold [1, 3, 2] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "Divide the letters from {'d': 7, 'f': 2} 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"
}
] | 6 | MATH |
[
{
"content": "Distribute the letters {'m': 2, 'e': 2, 'w': 4} among 2 distinguishable boxes with capacities [4, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "Given the letters {'p': 3, 'a': 2, 'd': 2}, place them into 2 indistinguishable boxes with sizes [2, 5]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "Given the letters {'w': 3, 'r': 3}, place them into 2 indistinguishable boxes with sizes [3, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "You have {'d': 5, 'y': 1, 'g': 2} and need to distribute them into 3 different boxes with capacities [3, 2, 3]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17 | MATH |
[
{
"content": "Given the letters {'u': 1, 'd': 4, 'y': 3}, place them into 3 labeled boxes with sizes [3, 3, 2]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 23 | MATH |
[
{
"content": "Arrange the letters {'l': 3, 'g': 4} into 3 uniquely identified boxes that can hold [1, 3, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "Distribute the letters {'j': 1, 'b': 2, 't': 4} among 2 distinguishable boxes with capacities [3, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "Given the letters {'u': 4, 'y': 5}, place them into 3 indistinguishable boxes with sizes [1, 2, 6]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "Arrange the letters {'k': 2, 'g': 1, 'h': 3} into 2 uniquely identified boxes that can hold [2, 4] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "Given the letters {'v': 4, 'n': 2, 'p': 4}, place them into 2 indistinguishable boxes with sizes [4, 6]. 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, 'h': 4} into 2 undistinguishable boxes with sizes [5, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Arrange the letters {'r': 2, 'a': 6} into 3 undistinguishable boxes with capacities [3, 2, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Distribute the letters {'i': 3, 'r': 4, 't': 3} among 3 distinguishable boxes with capacities [5, 3, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 49 | MATH |
[
{
"content": "Distribute the letters {'h': 3, 'z': 6} among 3 identical containers that can hold [3, 3, 3] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Distribute the letters {'r': 2, 's': 4} 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"
}
] | 5 | MATH |
[
{
"content": "Divide the letters from {'a': 1, 's': 2, 'r': 3} into 3 undistinguishable boxes with sizes [2, 2, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Distribute the letters {'a': 6, 'u': 3} among 3 distinguishable boxes with capacities [4, 3, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "Divide the letters from {'s': 3, 'g': 3, 'a': 2} into 2 distinctively labeled boxes with sizes [4, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Arrange the letters {'j': 5, 'd': 1, 's': 4} into 3 undistinguishable boxes with capacities [2, 3, 5]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 28 | MATH |
[
{
"content": "Given the letters {'e': 2, 'f': 3, 'p': 2}, place them into 3 labeled boxes with sizes [2, 2, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | MATH |
[
{
"content": "Given the letters {'f': 3, 'g': 3, 'r': 2}, place them into 2 labeled boxes with sizes [4, 4]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "You have {'m': 4, 'u': 6} and need to distribute them into 2 identical boxes with capacities [7, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Divide the letters from {'x': 3, 'u': 2, 'd': 2} into 2 undistinguishable boxes with sizes [4, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Arrange the letters {'a': 1, 'z': 2, 'v': 3} into 2 uniquely identified boxes that can hold [2, 4] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "Distribute the letters {'p': 2, 'm': 6} among 3 distinguishable boxes with capacities [4, 3, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "Arrange the letters {'e': 6, 'x': 3} into 2 undistinguishable boxes with capacities [6, 3]. 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 {'v': 3, 'd': 4} into 2 uniquely identified boxes that can hold [4, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "You have {'p': 3, 'i': 4} and need to distribute them into 2 different boxes with capacities [5, 2]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "You have {'n': 2, 'k': 2, 'a': 3} and need to distribute them into 2 different boxes with capacities [4, 3]. 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 {'s': 2, 'm': 3, 'r': 5} into 2 undistinguishable boxes with capacities [4, 6]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "Distribute the letters {'a': 2, 'n': 4, 'r': 3} among 3 distinguishable boxes with capacities [3, 2, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 39 | MATH |
[
{
"content": "You have {'q': 2, 'i': 3, 'z': 3} and need to distribute them into 2 different boxes with capacities [1, 7]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Arrange the letters {'x': 5, 'l': 5} into 3 undistinguishable boxes with capacities [6, 2, 2]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "Distribute the letters {'t': 5, 'h': 4} among 3 distinguishable boxes with capacities [4, 1, 4]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "Arrange the letters {'t': 2, 'l': 7} into 2 uniquely identified boxes that can hold [5, 4] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Given the letters {'x': 7, 'h': 3}, place them into 2 labeled boxes with sizes [5, 5]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Given the letters {'u': 4, 'i': 1, 'l': 3}, place them into 2 indistinguishable boxes with sizes [5, 3]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "Arrange the letters {'y': 3, 'q': 2, 'm': 1} into 2 undistinguishable boxes with capacities [2, 4]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "Divide the letters from {'t': 3, 'n': 4, 'i': 3} into 2 undistinguishable boxes with sizes [6, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13 | MATH |
[
{
"content": "Distribute the letters {'t': 1, 's': 4, 'b': 3} among 2 distinguishable boxes with capacities [3, 5]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "Given the letters {'m': 4, 'n': 2, 'g': 4}, place them into 3 labeled boxes with sizes [3, 4, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 55 | MATH |
[
{
"content": "Divide the letters from {'s': 7, 'z': 3} into 3 distinctively labeled boxes with sizes [1, 5, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "Divide the letters from {'m': 5, 'q': 4} into 2 distinctively labeled boxes with sizes [5, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "Given the letters {'a': 3, 'q': 6}, place them into 2 labeled boxes with sizes [4, 5]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Distribute the letters {'e': 4, 'q': 6} 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"
}
] | 13 | MATH |
[
{
"content": "Distribute the letters {'g': 2, 'k': 3, 'r': 2} among 3 distinguishable boxes with capacities [3, 3, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "Distribute the letters {'k': 3, 'f': 3} among 3 distinguishable boxes with capacities [3, 2, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "Arrange the letters {'w': 1, 'f': 5} into 2 uniquely identified boxes that can hold [3, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Given the letters {'n': 5, 'y': 4, 'v': 1}, place them into 3 indistinguishable boxes with sizes [4, 5, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 22 | MATH |
[
{
"content": "Distribute the letters {'q': 2, 'l': 1, 'b': 3} 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": "Distribute the letters {'y': 1, 'v': 3, 'j': 3} among 3 identical containers that can hold [3, 2, 2] letters respectively. How many different arrangements exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Arrange the letters {'v': 4, 'y': 1, 'a': 1} into 2 undistinguishable boxes with capacities [3, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Divide the letters from {'i': 3, 'v': 7} into 2 undistinguishable boxes with sizes [3, 7]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Given the letters {'d': 2, 's': 2, 'm': 3}, place them into 2 labeled boxes with sizes [3, 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 {'k': 2, 'p': 4}, 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"
}
] | 5 | MATH |
[
{
"content": "Given the letters {'b': 4, 'w': 4}, place them into 2 labeled boxes with sizes [5, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Arrange the letters {'i': 4, 'h': 4} into 2 undistinguishable boxes with capacities [6, 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 {'y': 2, 'd': 1, 'e': 3} 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": "Given the letters {'w': 2, 's': 2, 'f': 2}, place them into 3 labeled boxes with sizes [4, 1, 1]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "Arrange the letters {'k': 1, 'v': 3, 'm': 4} into 2 undistinguishable boxes with capacities [4, 4]. 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 {'y': 2, 'g': 4, 'z': 4} into 2 uniquely identified boxes that can hold [7, 3] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "You have {'e': 4, 'y': 4, 'd': 2} and need to distribute them into 3 different boxes with capacities [3, 3, 4]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 55 | MATH |
[
{
"content": "Divide the letters from {'c': 3, 'j': 1, 'g': 4} into 3 undistinguishable boxes with sizes [1, 2, 5]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13 | MATH |
[
{
"content": "Arrange the letters {'l': 4, 'p': 3} into 3 uniquely identified boxes that can hold [4, 2, 1] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "Arrange the letters {'k': 3, 't': 6} into 2 undistinguishable boxes with capacities [6, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Given the letters {'b': 3, 'e': 3}, 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"
}
] | 7 | MATH |
[
{
"content": "Given the letters {'p': 4, 'n': 3}, place them into 3 labeled boxes with sizes [1, 1, 5]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Divide the letters from {'w': 3, 'a': 3} into 2 undistinguishable boxes with sizes [4, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Divide the letters from {'z': 2, 'h': 3, 'c': 2} into 3 undistinguishable boxes with sizes [2, 2, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14 | MATH |
[
{
"content": "Distribute the letters {'p': 2, 'z': 4} among 3 distinguishable boxes with capacities [1, 4, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Given the letters {'x': 3, 'b': 4, 'z': 2}, place them into 2 labeled boxes with sizes [6, 3]. How many distinct arrangements are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "Arrange the letters {'v': 5, 'g': 1} into 3 uniquely identified boxes that can hold [2, 3, 1] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Distribute the letters {'m': 3, 'l': 3} among 2 distinguishable boxes with capacities [4, 2]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "You have {'m': 3, 't': 2, 'g': 1} 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": "You have {'a': 3, 'b': 3} and need to distribute them into 2 identical boxes with capacities [3, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "You have {'c': 3, 'b': 3} and need to distribute them into 2 identical boxes with capacities [3, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Arrange the letters {'c': 3, 'a': 7} into 2 undistinguishable boxes with capacities [5, 5]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "You have {'m': 2, 'z': 4} 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"
}
] | 5 | MATH |
[
{
"content": "Divide the letters from {'c': 4, 'f': 3} into 3 distinctively labeled boxes with sizes [2, 3, 2]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Given the letters {'e': 3, 'r': 2, 'f': 2}, place them into 2 indistinguishable boxes with sizes [5, 2]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "Divide the letters from {'g': 4, 'u': 4} into 3 distinctively labeled boxes with sizes [1, 3, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Divide the letters from {'v': 6, 'q': 3} into 2 distinctively labeled boxes with sizes [5, 4]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Distribute the letters {'y': 1, 'q': 3, 'e': 2} among 2 distinguishable boxes with capacities [5, 1]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Distribute the letters {'y': 4, 'o': 1, 'j': 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"
}
] | 2 | MATH |
[
{
"content": "Distribute the letters {'u': 5, 'h': 3, 's': 2} among 2 distinguishable boxes with capacities [5, 5]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "You have {'s': 4, 'i': 2, 'u': 3} and need to distribute them into 3 identical boxes with capacities [2, 4, 3]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 39 | MATH |
[
{
"content": "Arrange the letters {'b': 4, 'n': 4, 'v': 2} 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"
}
] | 43 | MATH |
[
{
"content": "Arrange the letters {'f': 2, 'q': 2, 'k': 2} into 2 undistinguishable boxes with capacities [3, 3]. Find the total number of possible distributions.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "You have {'i': 2, 'h': 8} and need to distribute them into 2 identical boxes with capacities [3, 7]. How many distinct distributions are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Divide the letters from {'c': 6, 'j': 1, 'g': 3} into 3 undistinguishable boxes with sizes [3, 4, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15 | MATH |
[
{
"content": "You have {'z': 1, 'm': 3, 'r': 3} 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"
}
] | 19 | MATH |
[
{
"content": "Given the letters {'b': 1, 's': 5}, place them into 2 indistinguishable boxes with sizes [5, 1]. In how many ways can you do this?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Arrange the letters {'v': 3, 'k': 2, 'n': 2} into 2 uniquely identified boxes that can hold [2, 5] letters respectively. Find the number of possible arrangements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "Divide the letters from {'l': 5, 'q': 3, 'm': 2} into 2 undistinguishable boxes with sizes [7, 3]. How many ways?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "Distribute the letters {'p': 5, 'u': 4} among 2 distinguishable boxes with capacities [3, 6]. How many different distributions exist?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "You have {'l': 5, 'x': 1, 'm': 4} and need to distribute them into 2 different boxes with capacities [3, 7]. In how many ways can this be done?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
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