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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.

 Dec 19, 2019
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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

 

 

cool cool cool

 Dec 19, 2019

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