Question

At a party everyone shook hands with everyone exactly once there were a total of 36 handshakes how many people were at t he party

Answer 1

combinations of n people r at a time
= n!/[ r! (n-r)! ]
n = ?
r = 2

36 = n!/[ 2 (n-2)! ]
72 = n! /(n-2)!
72 = n (n-1) the rest cancels
72 = n^2 -n
n^2 - n - 72 = 0
(n-9)(n+8) = 0
n = 9

Answer 2

combinations of n people r at a time
= n!/[ r! (n-r)! ]
n = ?
r = 2

36 = n!/[ 2 (n-2)! ]
72 = n! /(n-2)!
72 = n (n-1) the rest cancels
72 = n^2 -n
n^2 - n - 72 = 0
(n-9)(n+8) = 0
n = 9