One Choose n

Theorem

 * $\dbinom 1 n = \begin{cases} 1 & : n \in \left\{ {0, 1}\right\} \\ 0 & : \text {otherwise} \end{cases}$

where $\dbinom 1 n$ denotes a binomial coefficient.

Proof
By definition of binomial coefficient:


 * $\dbinom m n = \begin{cases}

\dfrac {m!} {n! \left({m - n}\right)!} & : 0 \le n \le m \\ & \\ 0 & : \text { otherwise } \end{cases}$

Thus when $n > 1$:
 * $\dbinom 1 n = 0$

and when $n < 0$:
 * $\dbinom 1 n = 0$

Then: