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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.