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nCr Definitions and Properties

Prove that ...

Question

Prove that $r!^{n} C_{r} =^{n} P_{r}$

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Solution

We have $^{n} C_{r} = \frac{n!}{(n - r)! r!}$ and $^{n} P_{r} = \frac{n!}{(n - r)!}$ .
So it is clear that $^{n} P_{r} = r!^{n} C_{r}$ .

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