Everybody in a room shakes hands with everybody else.

B. 12

Explanation:

We know that,

nCr

$=\frac{n !}{r !(n-r) !}$

Let total time of handshakes=nC2 = 66

$\frac{n !}{2 !(n-2) !}=66$

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

⇒ n2-n=132

⇒ (n-12) (n+11) = 0

n=12 or n = – 11

Therefore, n = 12

Hence, Option (B) 12 is the correct answer.