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In the proof of $p$ | $\binom{p}{k}$ (p divides $\binom{p}{k}$) where $p$ is prime,

what is the simplest way to show that $${(p-1)! \over (k)!(p-k)!}$$ is an integer?

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Multiply the numerator by $p$ to get $\binom{p}{k}$, a natural number and note that the denominator can't have $p$ as its factor.

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