Question

Four people in a room. Each shakes hands with each of the others once. How many handshakes are there?  
6
10
12
16
22

Answer 1

Combinations problem. We just have to reword it. If one guy is to shake hands with another guy, then how many pairs can we possibly have? Order in which the guys shake hands doesn't matter, so we use combinations. We choose 2 from 4.

4C2=4!/[(4-2)!*2!]=24/(2*2)=6 handshakes