Expressions reducible to factorial form

Question

Can the following expression be written as the factorial of $m$?

$m(m-1)(m-2) \dots {m-(n-1)}$

Answer 1

No, but you can write $$m(m-1)(m-2) \dots {m-(n-1)}=\frac {m!}{(m-n)!}$$ Note which factors are missing from $m!$ in your original expression

Answer 2

$$m(m-1)\cdots (m-n+1) = \frac{m(m-1)\cdots (m-n+1)(m-n)!}{(m-n)!} = \frac{m!}{(m-n)!}$$