Combinatorics ')

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? 

I assume \( \dfrac{12\cdot 10}{2}=60 \text{ hand shakes}\)

Every person    shakes  hands with  10  other people

So...  12 * 10   =  120

But handshake  A - C   is the same as handshake  C  - A

So...we need to  divide this by 2

So  120 / 2   = 60  handshakes