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Math

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At a party, 55 handshakes took place as everyone shook hands with everyone else in attendance. How many people were at the party?

  • Math - ,

    For n people the number of handshakes would be
    C(n,2)
    so
    n!/(2!(n-2)!) = 55 , where n is a positive integer.

    n(n-1)/2 = 55
    n(n-1) = 110
    n^2 - n - 110 = 0
    (n-11)(n+10) = 0

    n = 11

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