Question

Everybody in a room shakes hands with everybody else. The total number of hand shakes is $66$. Then 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 $n$ perrons in the room.

The total number of hand shakes is the same as the number of ways of selecting $2$ out of $n$.

$\because {}^n{C}_2=66\Rightarrow \frac{n(n-1)}{2!}=66$

$\Rightarrow n^2-n-32=0\Rightarrow (n-12)(n+11)=0$

$\therefore n=12$