8 people attend a party. During the party everyone shakes hands with everyone else. How many handshakes take place at the party?
I notice that each person shakes hands with 7 other people, since they don't shake hands with themselves. But if I just multiply 8 by 7, I would be double-counting each handshake, since A shaking hands with B is the same as B shaking hands with A. So I need to divide by 2 to avoid double-counting. Therefore, the number of handshakes is 8 times 7 divided by 2, which is 28. 