Suppose there are n people in the party. The first person shakes hand with the other (n-1) guests. The second guest shakes hand with the other (n-2) guests. this will continue until the (n-1) th guest shakes hand with the nth guest.
Total number of handshakes is (n-1) + (n-2)... + 3 + 2 + 1.
For example, 6 people in a party shake hand with other guests. So how many handshakes will be there?