At a party , everyone shook hands with everybody else. There were 66 handshakes . How many people were there in the party ?
A
13
B
11
C
10
D
12
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