## Thinking Mathematically (6th Edition)

Let's look at the handshakes of each person, one by one, without mentioning the same handshake twice. Person 1 shakes hands with person 2, 3, 4, and 5. Person 2 also shakes hands with person 3, 4, 5. Person 3 also shakes hands with person 4, 5. Person 4 and person 5 shake hands. The total number of exchanged handshakes is $4+3+2+1=10$.