Question

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?
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

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