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Question 17
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?
[CAT 2004]
Solution
Total number of pairs is $$^{N}C_2$$. Number of pairs standing next to each other = N. Therefore, number of pairs in question = $$^{N}C_2$$ - N
= 28/2 = 14.
If N = 7,
$$^{7}C_2$$ - 7 = 21 - 7 = 14.
N = 7.
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