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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Binomial Theorem

NDA 2022 · Mathematics · Binomial Theorem

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

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

Options

  1. A00
  2. B17\frac{1}{7}
  3. C12\frac{1}{2}
  4. D11

Correct answer

A. 00

Step-by-step solution

nC7=n!(n−7)!7!=n(n−1)(n−2)(n−3)(n−4)(n−5)(n−6)7!\begin{aligned} & { }^{\mathrm{n}} C_7=\frac{n!}{(n-7)!7!} \\ & =\frac{n(n-1)(n-2)(n-3)(n-4)(n-5)(n-6)}{7!} \end{aligned} is not divisible by 7 for n>7∴n(E)=0⇒P(E)=0n > 7\therefore \quad n(E)=0 \quad \Rightarrow P(E)=0
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