Question

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

Answer 1

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