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A handshake is an unordered pair, since A shaking hands with B is the same event as B shaking hands with A, so this is 10C2 = (10 × 9)/2 = 45. The 90 option is 10P2, the ordered count, and it is exactly double — which is what happens when the order question is answered wrongly, and it is the option placed first for that reason. 100 is 10 × 10, which counts each person shaking hands with themselves as well. And 20 is 2 × 10, a guess with no counting model behind it.