HMMT 十一月 2009 · GEN2 赛 · 第 7 题

英文解析

7. [ 4 ] Five guys are eating hamburgers. Each one puts a top half and a bottom half of a hamburger bunon the grill. When the buns are toasted, each guy randomly takes two pieces of bread off of the grill.
   What is the probability that each guy gets a top half and a bottom half?
   Answer: Say a guy is content if he gets a top half and a bottom half. Suppose, without loss of 8
   generality, that the first guy’s first piece of bread is a top. Then there is a chance that his second 563
   piece of bread is a bottom. By the same reasoning, given that the first guy is content, there is a 49
   chance that the second guy is content. Given that the first two guys are content, there is a chance 37
   5 4 3 2 1 85
   that the third guy is content, and so on. Our final answer is · · · · = .
   9 7 5 3 1 63