ThmDex – An index of mathematical definitions, results, and conjectures.
F12193
Formulation 1
Let $n, m \in \mathbb{N}$ each be a D996: Natural number.
Then
(1) \begin{equation} m > n \quad \implies \quad \binom{n}{m} = 0 \end{equation}
(2) \begin{equation} m \leq n \quad \implies \quad \binom{n}{m} = \frac{n !}{(n - m) ! m !} \end{equation}