Question

Everybody in a room shakes hands with every body else. The total number of hand shakes is 66. The total number of persons in the room is –

• A. 11
• B. 12
• C. 13
• D. 14

Answer 1

Answer: (B)

12

Answer 2

Let no. of persons be n

no. of hand shakes = ⁿC₂

ⁿC₂ = 66, $\frac{n(n - 1)}{2}$ = 66

n² – n – 132 = 0

n = –11, 12

n = 12 (n = – 11 impossible)