Every body in a room shakes hands with everybody 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

Solution:

Let total number of persons be n.
Since, total number of hand shakes = 66

$\begin{array}{lrl} ∴^{n} C_{2} = 66 \Rightarrow \frac{n (n - 1)}{2} = 66 \\ \Rightarrow n^{2} - n - 132 = 0 \Rightarrow (n - 12) (n + 11) = 0 \\ \Rightarrow n = 12 [∵ n cannot be negative] \end{array}$

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