网球平分计数

Tennis Deuces I

个人笔记

网球计分依次为 0、15、30、40。

问：有多少种不同的得分过程能使比赛恰好到达 40-40（deuce，平分）？

How many ways are there to get a score of $40 - 40$ (deuce) in tennis? Scores in tennis follow $0, 15, 30, 40$ .

解析

到达 40 意味着赢了 3 分。到达 40-40 等价于双方在前 6 分里各赢 3 分。

因此方式数为

\binom{6}{3}=20.

Reaching 40 means winning 3 points. Reaching 40-40 is equivalent to each side winning 3 of the first 6 points.

So the number of ways is

\binom{6}{3}=20.