HMMT 二月 2008 · COMB 赛 · 第 3 题

英文解析

3. [ 4 ] Farmer John has 5 cows, 4 pigs, and 7 horses. How many ways can he pair up the animals so that every pair consists of animals of different species? Assume that all animals are distinguishable fromeach other. (Please write your answer as an integer, without any incomplete computations.)
   Answer: 100800 Since there are 9 cow and pigs combined and 7 horses, there must be a pair with 1
   cow and 1 pig, and all the other pairs must contain a horse. There are 4 × 5 ways of selecting the cow-pigpair, and 7! ways to select the partners for the horses. It follows that the answer is 4 × 5 × 7! = 100800.