Combination is defined as $C(n,k) = \dfrac{n!}{k!(n-k)!}$, where $n$ and $k$ are non-negative integers.
Now, the definition can be extended to $C(r,k)$, where $r$ is real number and $k$ is an integer: $$ C(r, k) = \cases{ \frac{r(r-1)\cdots(r-k+1)}{k!} & $k \ge 0$ \\ 1 & $k = 0$ \\ 0 & $k < 0 $} $$
Question: what is the usage, or application cases, that such definition extension could help? I just don't see the real number $r$'s usage.