If n>7, then what is the probability that C(n, 7) is a multiple of 7?

NDA 2022 Mathematics question

If , then what is the probability that is a multiple of 7?

(A)
(B)Correct
(C)
(D)

Answer: (B)

Solution

. Among the 7 consecutive integers in the numerator exactly one is a multiple of 7, namely with ; the other six factors, divided by , leave a number that is

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Question ID VK-029514