Browse Questions

If one person shakes hand with another only once,the no. of hand shakes is 66. How many persons are there?

$\begin{array}{1 1} 10 \\ 12 \\ 24 \\ 33 \end{array}$

Let there be $n$ persons.
Each hand shakes with other only once.
$\therefore$ No. of hand shakes = $^nC_2=66\:(given)$
$\large\frac{n(n-1)}{2}$$=66$
$\Rightarrow\:n^2-n-132=0$
$\Rightarrow\:(n-12)(n+11)=0$
$\Rightarrow\:n=12\:or\:-11\:(not \:possible)$
The no. of persons =$12$