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

Step-by-step solution

Let the number of persons in the room be n , then array rlr & ^n C₂=66 & n(n-1) 2 & =66 & n^2-n-132 & =0 & (n-12)(n+11) & =0 & n & =12 array ( n -11)