How many handshakes occurred?

Fifteen knights were invited to a meal at the castle in Belmar. Before sitting down, each of the fifteen knights shook hands with each of the other knights. How many handshakes occurred?

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The first knight shakes hands with 14 other knights, the second knight having already shaken hands with the first, shakes 13 hands and so on. 14+13+12+11+10+9+8+7+6+5+4+3+2+1 = 105

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