Question

Every body in a room shake hands with everybody else only once. If the total number of handshakes is $66$ then number of persons in the room is

• A. 11
• B. 12
• C. 13
• D. 14

Answer 1

The correct option is B 12

Number of hand shake in between $n$ people are $=$ Total Number of hand shake between any two person. So we have $n$ people we have to pick $2$ persons. So total number of hand shakes are${=}^n{C}_2$ because we have to choose $2$ from $n$.

So, number of Hand Shakes $=\frac{n(n-1)}{2}$

Total Hand Shakes $=66$

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

$\Rightarrow n(n-3)=132$

$\Rightarrow n=12$