Short answer: 3240 handshakes.
Remark
If you watch hockey, you've actually seen this happen. After the game, the winning team will stay on the ice usually on center ice. As you look at them, the man on your right will go down the line and rough up or shake hands or say something to each of his teammates on the line. Then he goes into the dressing room. So he has talked to n - 1 people. The next person going down the line will talk to n - 2 people. and so on all the way down the line.
Formula
Sum = (n + 1)*n/2 is what the formula is.
Givens
n = 80
Sub and Solve
Sum = (80 + 1)*80 / 2
Sum = 81 * 40
Sum = 3240 handshakes.<<<<< Answer