Answer to Question #140988 in Discrete Mathematics for Ellya Camiling

Question

In a group of 25 people, there is a ____ chance that at least two of them has shaken hands with the same number of people.

Answer 1

Now if there is a person who hasn't shaken hands with anybody, then there cannot be any person who has shaken hands with all. So number of different handshakes can vary either from 0 to 23 or 1 to 24. So in total there can be at most 24 different number of times a person can shake hand. So by Pigeon hole principle two men must shake hands equal number of times. Hence the chance is 100 percent.