Question

Everybody in a room shakes hands with everybody else. The total number of handshakes is 45. The total number of persons in the room is

• A. 9
• B. 10
• C. 5
• D. 15

Answer 1

The correct option is B 10

Let total number of persons be $n$.
Then, ${}^n{C}_2=45$
$\Rightarrow \frac{n(n-1)}{2}=45$
$\Rightarrow n^2-n-90=0$
$\Rightarrow n=-9,10$
Rejecting $n=-9$, we get $n=10$