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?
Explanation:
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).
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