1260.02 – Handshakes (n)

At a voter registration meeting everybody shook hands exactly once with everybody else. How many handshakes took place? (It'll be a formula, not a number, of course.)

Solution

If there were $n$ people at the meeting, each one shook hands $n-1$ times. Then it would seem that there were $n(n-1)$ handshakes. But if person $A$ shook hands with person $B$ , remember that $B$ also shook hands with $A$ . So the formula $n(n-1)$ is counting each handshake twice. So the formula for $n$ people is $\dfrac{n(n-1)}{2}$ handshakes.