SOLUTION: There are five people in the room. Each person shakes the hand of every other person exactly once. How many handshakes are exchanged?

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all 5 people shake hands with 4 other people

BUT ... Jim shaking hands with Sue is the same as Sue shaking hands with Jim

so, the total number of handshakes is (5*4)/2 or 10



this is a combination of 5 things taken 2 at a time ... 5C2