Binomial Coefficient/Examples/2 from -5

Example of Binomial Coefficient

 * $\dbinom {-5} 2 = 15$

Proof
From the definition of binomial coefficient:


 * $\dbinom r k = \begin {cases}

\dfrac {r^{\underline k} } {k!} & : k \ge 0 \\ & \\ 0 & : k < 0 \end {cases}$ where $r^{\underline k}$ denotes the falling factorial.

Therefore: