WBJEE · Maths · Permutation Combination
Product of any \(r\) consecutive natural numbers is always divisible by
- A \(\mathrm{r}\) !
- B \((r+4) !\)
- C \((r+1) !\)
- D \((r+2) !\)
Answer & Solution
Correct Answer
(A) \(\mathrm{r}\) !
Step-by-step Solution
Detailed explanation
Hints : \((n+1)(n+2) \ldots \ldots .(n+r)\) \[ \begin{aligned} & =\frac{(n+r) !}{n !} \\ & =\frac{(n+r) !}{n ! r !} r !=r !^{n+r} C_n \end{aligned} \]
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