If each of seven persons in a group shakes hands with each of the other six persons then a total of forty-two handshakes occurs?

The answer is 21 handshakes because the first person shakes hands with the other 6 people. The second person shakes hands with 5 people because they already shook hands with the first person. The third person shakes hands with 4 people because they already shook hands with the first and second person. The fourth person shakes hands with 3 people because they already shook hands with the first, second, and third. The fifth person shakes hands with 2 people because they already shook hands with the first, second, third, and fourth person. The sixth person shakes hands with the seventh person because the rest have already shaken hands with them. The seventh person doesn't have anyone else to shake hands with.

Therefore the answer is 21 handshakes.