10个人可以分成两组，每组5个人，有多少种方式？
在数学中，排列被称为排列一个集合的过程，其中一个集合的所有成员被排列成一些系列或顺序。如果集合已经排列，则排列的过程称为对其组件的重新排列。几乎所有数学领域都以或多或少的重要方式发生排列。当考虑某些有限集上的不同命令时，它们经常出现。
什么是组合？
组合是从组中选择项目的行为，这样（不像排列）选择的顺序无关紧要。在较小的情况下，可以计算组合的数量。组合是指一次取k个不重复的n个事物的并集。组合可以以任意顺序选择项目。对于那些允许重复出现的组合，经常使用术语 k-selection 或 k-combination with replication。
置换公式
在排列中，从 n 个事物的集合中选择 r 个事物，没有任何替换。在这个选择的顺序。
nPr = (n!) / (n-r)!
Here,
n = set size, the total number of items in the set
r = subset size , the number of items to be selected from the set
组合配方
组合 r 个事物是从一组 n 个事物中选择的，其中选择的顺序无关紧要。
nCr = n!/(n−r)!r!
Here,
n = Number of items in set
r = Number of items selected from the set
10个人可以分成两组，每组5个人，有多少种方式？
解决方案：
The first group can be chosen in 10C5 = 252 ways. There is just 1 way of choosing the second and final group from the 5 people who now remain.
In the process described above, every possible way of dividing 10 people into 2 group of 5 people each has been counted 2! = 2 times.
So the number of ways of dividing a group of 10 people into 2 group of 5 people each
= 252⁄2
= 126
类似问题
问题1：8个人分成两组，每组四人，有多少种不同的方式。
解决方案：
The first group can be chosen in 8 C 4 = 70 ways. There is just 1 way of choosing the second and final group from the 4 people who now remain.
In the process described above, every possible way of dividing 8 people into 2 group of 4 people each has been counted 2! = 2 times.
So the number of ways of dividing a group of 8 people into 2 group of 4 people each
= 70⁄2
= 35
问题 2：8 人一组可以分成 4 组，每组 2 人，有多少种不同的方式？
解决方案：
The first team can be chosen in 8 C 2 = 28 ways. Having done that, there are 6 people left and the second team can be chosen from them in 6 C 2 = 15 ways.
After that there are 4 people left and the third team can be chosen from them in 4 C 2 = 6 ways. There is just 1 way of choosing the fourth and final team from the 2 people who now remain.
In the process described above, every possible way of dividing 8 people into 4 teams of 2 people each has been counted 4! = 24 times.
So the number of ways of dividing a group of 8 people into 4 teams of 2 people each
= 28 * 15 * 6 / 24
= 105