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At a party , everyone shook hands with everybody else. There were 66 handshakes . How many people were there in the party ?

At a party , everyone shook hands with everybody else. There were 66 handshakes . How many people were there in the party ? Correct Answer 12

Let the number of people be x For a handshake we need 2 people so selecting 2 person form x can be done in xC2 ways. Therefore xC2 = 66 x!/(x - 2)!2! = 66 x(x - 1)/2 = 66 x(x - 1) = 132 Solving this we get x = 12

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