Question

Everybody in a room shakes hands with everybody else. If number of hand shakes is $66$. Then total number of persons in the room is

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

Answer 1

Answer: (A)

$12$

Let number of person in the room is $n$.

Then if everybody shakes hands with everybody else then number of hand shakes is ${}^n{C}_2$.

According to the problem,

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

or, $n(n-1)=132$

or, $n^2-n-132=0$

or, $(n+11)(n-12)=0$

or, $n=12$. [ Since $n\ne -11$]

So total number of person in the room is $12$.