Q253 / 270 · NDA 2022 (Phase 2) · Mathematics

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

  • Correct answer
    A
    $0$
  • B
    $\frac{1}{7}$
  • C
    $\frac{1}{2}$
  • D
    $1$

Solution

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

Hence, the correct answer is option: 'A'.

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