Aptitude 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, $= \dfrac{n(n-3)}{2}$

$⇒\dfrac{n(n-3)}{2}= \dfrac{60}{3}$

$⇒\dfrac{n(n-3)}{2}= 20$

$⇒ n(n-3)= 40$

$⇒n = \textbf{8}$

**Amit Bikram**

*()
*

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