if 15 people met at a party and all shook hands with one another, how many hand shakes would there be? (assume no one shakes the same hand twice?

Answer 1

the first person shakes 14 hands.
The second person also shakes 14 hands, but he's already shaken hand #1, leaving only 13 other hands.

Continuing, we see that the total unique hands shaken is 14+13+12+...+1 = 14*15/2 = 105