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    OlympiadEasyCombinatorics7–9

    Handshake Problem

    Problema do Aperto de Mão

    In a room of 10 people, everyone shakes hands with everyone else exactly once. How many handshakes occur?

    Each pair of people shakes hands once. Use \binom{n}{2}.

    Solution

    Step 1 of 2

    1. 1.The general form is \binom{n}{k} = \frac{n!}{k!\,(n-k)!}, so with n = 10 and k = 2 the second factorial is (10 - 2)! = 8!.