单场淘汰赛-可能的组合数量 [英] A single elimination tournament - number of possible combinations

问题描述

有8个人参加一场淘汰赛的组合次数是多少？总的比赛次数为7，但我还需要此组合可以组合的数量

What are the number of combinations in which 8 persons taking part in a single elimination tornament play? Total no of matches played would be 7 but I also need the number of combinations that can for this set

推荐答案

如果没有，不管玩家在树上的哪个位置开始比赛，而仅与他/她与哪个对手战斗以及他/她得到多长时间，我们都可以说左边的玩家总是获胜，然后只需计算创建最底行的方式数量即可，这是8！ 40320。

If it doesn't matter where in the tree a player starts, but only which opponents he/she fights, and how long he/she gets, we can say that the left player always wins and then just calculate the number of ways to create the bottom most row, which is 8! 40320.

第一种可能性：

       a
   a       e
 a   c   e   g
a b c d e f g h

第二种可能性：

       a
   a       e
 a   c   e   h
a b c d e f h g

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