If seven people meet each other and each shakes hands only once, how many handshakes will there have been?

Question

If seven people meet each other and each shakes hands only once with each of the others, how many handshakes will there have been?

Answer 1

The first of the 7 people will shake hands with 6 others. Only 6 because no person is going to shake hands with themselves. The second person also shakes hands with 6 people, but you have already counted one of those handshakes, namely the one with the first person. Therefore, the second person shakes hands with only 5 NEW people. Then the third person adds 4 new handshakes, etc., down to the 2nd to the last person who adds 1 new handshake. The last person has no one new, so all of the last person's handshakes are already counted. In summary:

6+5+4+3+2+1=21

Answer 2

7*6/2=21 handshakes