CAT 2004QA Question 4

Forming a committeeEasy

N persons stand on the circumference of a circle at distinct points. Each possible pair of persons, not standing next to each other, sings a two-minute song one pair after the other. If the total time taken for singing is 28 minutes, what is N?

Answer & solution

  • A

    5

  • 7

  • C

    9

  • D

    None of the above

Solution

Total time taken for singing = 28 minutes

∴ Total songs sung = 14

As there are N persons, the total number of songs sung

NC2 – (those sung between adjacent persons) = NC2 – N

∴ N!(N-2)!×2! - N = 14

∴ N2-3N2=14

∴ (N – 7)(N + 4) = 0

∴ N = 7

Hence, option (b).

CAT 2004 QA Q4: N persons stand on the circumference of a circle at distinct points. Each possible pair of persons, not standi — Solution | TheCATExam