Is this identity known and if so, does it have a name?

Question

$$\frac{a!}{b!} = \begin{cases} \prod_{k=0}^{a-b-1} (a-k) &\ \ a > b \\ \\ 1\div\prod_{k=0}^{b-a-1} (b-k) & \ \ a<b\\ \end{cases}$$

Furthermore, if it is known, does it hold any relevance?

Answer 1

It is one way of expressing the falling factorial.