Every body 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 total number of persons be n.Since, total number of hand shakes = 66    ∴    nC2    =66⇒n(n−1)2=66⇒    n2−n−132    =0⇒    (n−12)(n+11)    =0⇒        n    =12    [∵n cannot be negative ]