There are 6 married couples at a party. At the start of the party, every person shakes hands once with every other person except his or her spouse. How many handshakes are there?

There were 60 handshakes.

Note that the first couple each shake 10 hands

The next couple each shake 8 hands

The next each shake shake 6 hands....etc.

So 2 * (10 + 8 + 6 + 4 + 2) = 60 handshakes

Thats what I did but I can't explain some things really well, so thanks CPhill.