[JEE Advanced 1985] The product of any $r$ consecutive natural numbers is always divisible by $r!$.
The product of any $r$ consecutive natural numbers is always divisible by $r!$.
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· 1mo ago
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Answer: True.
The product of $r$ consecutive naturals starting at $n+1$ is $\frac{(n+r)!}{n!}=r!\binom{n+r}r$, a multiple of $r!$.
JEE Advanced 1985 · Permutations and Combinations — verified solution by the Vidaara Team.
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