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