SOLUTION: There are 12 people in a room. Each person will shake hands with everyone else just once. How many handshakes will there be. (Joe shaking hands with Bob is the same as Bob shaki

Question 437779: There are 12 people in a room. Each person will shake hands with everyone else just once. How many handshakes will there be. (Joe shaking hands with Bob is the same as Bob shaking hands with Joe.) Through exhaustive listing I came up with 65...is this correct? Thanks!
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
With 12 people (or 12 elements in a set), we need to choose a subset of two different "elements" where order does not matter. Also, we need to choose all such subsets because each person is shaking hands with everyone else exactly once. The number of ways is .
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