Question

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

Answer 1

let there are n people's
by using combination concept :
nC2 = 66
solve for n

Answer 2

The first person shakes hands with n others, the second with n-1, the third with n-2 and so on until the second last shakes hands with only one other person. So we need to know the value of n such that the sum of n, n-1, n-2, n-3 etc = 66. Therefore n =11

Answer 3

nC2 = 66
n!/(n-2)!2! = 66
n(n-1)(n-2)!/(n-2)!2! = 66
cancel out for (n-2)!, it can be
n(n-1)/2 = 66
n(n-1) = 2 * 66
n(n-1) = 12 * 11
n(n-1) = 12 * (12-1)
so, n = 12

Answer 4

thanks