# Difficult Permutation-Combination Solved QuestionAptitude Discussion

 Q. Some boys are standing on a circle at distinct points. Each possible pair of persons, who are not adjacent, sing a 3 minute song, one pair after another. The total time taken by all the pairs to sing is 1 hour. Find the number of boys?
 ✖ A. $6$ ✖ B. $7$ ✔ C. $8$ ✖ D. $9$

Solution:
Option(C) is correct

Each boy would pair with $n-3$ other boys

Number of possible pairs, $= \dfrac{n(n-3)}{2}$

$⇒\dfrac{n(n-3)}{2}= \dfrac{60}{3}$

$⇒\dfrac{n(n-3)}{2}= 20$

$⇒ n(n-3)= 40$

$⇒n = \textbf{8}$

## (1) Comment(s)

Amit Bikram
()

Why can't the no of pairs equals to $nC1*(n-3)C1$