There are 3 people at a party If each person must shake hands with every other person at the party exactly once how many handshakes will there be?

With 3 people, there are only 3 handshakes: AB, AC, and BC.

Where it gets interesting is at a party with, say, 10 people ... 45 handshakes.

Or in the US Senate when all 100 Senators are present ... 4,950 handshakes.