At the national curling championships, there are three teams of four players each. After the championships are over, the very courteous participants each shake hands once with every member of the opposing teams, and once with each member of their own team.
How many handshakes are there in total?
Let's start by making the question a bit simpler.
There are 12 people who shake hands once with each other. How many handshakes are there?
Another way of looking at this problem is how many ways can we choose 2 people?
There are 12 ways to choose the first person and 11 ways to choose the second person.
12*11 = 132
However, we must remember that choosing person a first and then person b is the same as choosing person b first, then person a.
So, we divide by 2.
132/2 = 66
Our final answer is 66 handshakes.
I hope this helped. :)))