Q65 / 120 · VITEEE 2007 · Mathematics

Everybody 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
    9
  • Correct answer
    B
    12
  • C
    10
  • D
    14

Solution

Let there are $\mathrm{n}$ persons in the room. The total number of hand shakes is same as the number of ways of selecting 2 out of $\mathrm{n}$. $\begin{array}{l} \therefore{ }^{n} C_{2}=66 \Rightarrow \frac{n(n-1)}{2 !}=66 \\ \Rightarrow n^{2}-n-132=0 \\ \Rightarrow(n-12)(n+11)=0 \Rightarrow n=12 \end{array}$

Hence, the correct answer is option: 'B'.

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