HMMT 二月 2008 · GEN1 赛 · 第 3 题

HMMT February 2008 — GEN1 Round — Problem 3

个人笔记

[ 3 ] There are 5 dogs, 4 cats, and 7 bowls of milk at an animal gathering. Dogs and cats are distinguishable, but all bowls of milk are the same. In how many ways can every dog and cat be paired witheither a member of the other species or a bowl of milk such that all the bowls of milk are taken?
2 2 4 4 17

解析

[ 3 ] There are 5 dogs, 4 cats, and 7 bowls of milk at an animal gathering. Dogs and cats are distinguishable, but all bowls of milk are the same. In how many ways can every dog and cat be paired witheither a member of the other species or a bowl of milk such that all the bowls of milk are taken?
Answer: 20 Since there are 9 dogs and cats combined and 7 bowls of milk, there can only be onedog-cat pair, and all the other pairs must contain a bowl of milk. There are 4 × 5 ways of selecting thedog-cat pair, and only one way of picking the other pairs, since the bowls of milk are indistinguishable,
so the answer is 4 × 5 = 20.
2 2 4 417