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排列组合问题原文如下Ten children are to be divided into an A team and

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排列组合问题
原文如下
Ten children are to be divided into an A team and a B team of 5 each.The A team
will play in one league and the B team in another.How many different divisions are
possible?
(翻译:10个孩子分成A,B两队,每队5个人,两队之间做对抗,有多少种分法?)
Solution.There are10!/(5!)= 252 possible divisions.
第二题是
In order to play a game of basketball,10 children at a playground divide themselves
into two teams of 5 each.How many different divisions are possible?
(翻译:10个孩子分成2个对打篮球,每队5个人,有多少种分法?)
Solution.Note that this example is different from Example 5b because now the order
of the two teams is irrelevant.That is,there is no A and B team,but just a division
consisting of 2 groups of 5 each.Hence,the desired answer is
(翻译:注意这个例子和上个例子不同的地方是这两个队互不相关,没有A,B两队,只分成2个各包含5人的组)
(10!/(5!))/2!= 126 .
第一题和第二题为什么不同?
我没看懂,不都是分成两组吗?一组5个人.
第一题的2队是分别有编号A,B的
比如【A队成员1,2,3,4,5号,B队成员6,7,8,9,10号】
与【B队成员1,2,3,4,5号,A队成员6,7,8,9,10号】属于2种不同分法
而第二题上面的分法看成是重复的分法,也就是属同一种