Everybody in a room shakes hands with everybody else. The total number of hand shakes is 66. The total number of persons in the room is?

Let there be n persons in the room. The total number of hand shakes is same as the number of ways of selecting 2 out of n.
ⁿC₂ = 66
⇒ n(n - 1) / 2! = 66
⇒ n² - n - 132 = 0
⇒ (n - 12) (n + 11) = 0
∴ n = 12