Question

Every body in a room shakes hands with every body else. The total number of hand shakes is $66$. The total number of persons in the room is

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

Answer 1

Answer: (B)

$12$

According to handshake problem,

let n=total number of person

So,

$\begin{array}{c}\frac{n\left(n-1\right)}{2}=66\\ n\left(n-1\right)=2\times 66\\ n\left(n-1\right)=2\times 6\times 11\\ n\left(n-1\right)=12\times 11\\ So,\\ n=12\end{array}$

Thus Option B