Question

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

• A. $11$
• B. $12$
• C. $13$
• D. $14$

Answer 1

The correct option is B $12$

Let there be 'n' people in the room.

The total number of handshakes between

a pair of people is similar to selecting

how many pairs of people in the group

This value is ${}^n{C}_2$

Given that ${}^n{C}_2=66$

$\frac{n(n-1)}{2}=66$

$n(n-1)=132=12\times 11$

$n=12$