10 people attend a party. During the party everyone shakes hands with everyone else. How many handshakes take place at the party?
I need to count the number of pairs of people who shake hands, without counting any pair twice. One way to do this is to use a formula for the number of ways to choose two items from a set of n items, which is n choose 2, or n(n-1)/2. In this case, n is 10, so the number of handshakes is 10 choose 2, or 10(10-1)/2. Simplifying, I get 10(9)/2, or 45.

