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jmc

prealgebra senior

Problem

Five couples were at a party. If each person shook hands exactly once with everyone else except his/her spouse, how many handshakes were exchanged? (Note: One obviously doesn't shake hands with oneself.)
Solution
There are a total of 10 people at the party. Each shakes hands with everyone else, except for their spouse, which will be a total of other people. The total number of handshakes will be , where we divide by 2 to correct for counting each handshake twice.
Final answer
40