Find all possible values of r such that: nPr = r!

Question

$$^{n}P_{r} = r!$$ Find all possible values of r.

Answer 1

You can go back to the definition.

$$^{n}P_{r} = r!\iff \frac{n!}{(n-r)!}=r!\iff \frac{n!}{(n-r)!r!}=1\iff\binom{n}{r}=1.$$