1260.01 – Handshakes (24, 1)

Twenty-four people are at a party. Each person shakes hands once with each other person. How many handshakes are there?

Solution

Each of the 24 people shakes hands 23 times, so our first thought might be that there are $24 \times 23$ handshakes.

But on second thought, we realize that $A$ shaking hands with $B$ is the same handshake as $B$ shaking hands with $A$ , so we only have half as many handshakes: $\dfrac{24 \times 23}{2} = 276$ handshakes (still a lot!).