Binomial Coefficient/Examples/5 from 2
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Example of Binomial Coefficient
- $\dbinom 2 5 = 0$
Proof
From the definition of binomial coefficient:
- $\dbinom n k = \begin{cases} \dfrac {n!} {k! \paren {n - k}!} & : 0 \le k \le n \\ & \\ 0 & : \text { otherwise } \end{cases}$
Here we have $k = 5$ and $n = 2$.
As $k > n$:
- $\dbinom 2 5 = 0$
$\blacksquare$