How many handshakes will happen if 100 people walk into a room and none of them have ever met before? Assume that everyone shakes hands with every other person exactly once.

Guest Dec 19, 2019

#1**+1 **

Note that if we had 3 people, A, B , C.....the number of handshakes = 3

AB AC

BC

Note that if we only had 4 people, A,B, C, D.....the number of handshakes = 6

AB AC AD

BC BD

CD

This implies that for n peole, the number of handshakes is n ( n - 1) / 2

So....for 100 people we have

100 (100 - 1) / 2 =

50 * 99 =

4950 handshakes

CPhill Dec 19, 2019