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Prove using induction that the binomial coefficient $\binom nr$ is always a natural number for all $n$ and for $0≤ r ≤ n$

I tried proving it but i failed .what should i do?

Abdullah Alfaqir
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    Can you post what you've tried? Also do you mean $\binom{n}{r}$? Finally, this is useful: https://en.wikipedia.org/wiki/Pascal%27s_rule – Alex R. Jun 04 '17 at 17:43
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    Since $\binom{n-1}r$ and $\binom{n-1}{r-1}$ are integers, $\binom nr$ is an integer if $0<r<n$. – peterwhy Jun 04 '17 at 17:48
  • I tried base step n=1 and r=1 the second step assumed that (nr) is a natural number then tried to prove if so then (n+1 r) is also a natural number using (n+1 r)=(n r-1)+(n r) – Abdullah Alfaqir Jun 04 '17 at 17:48
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    Consider Pascal's triangle, the base cases should be all the $1$'s, i.e. when $r = 0$ or $r = n$. Then induce for $n = 2, 3, \ldots$ onwards for those $\binom nr$ that are not base cases, i.e. for $0<r<n$. – peterwhy Jun 04 '17 at 17:52

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