If $n$ is an $\underline{\text{integer}}$ > 7, prove that $\big(^n_7\big) - { \begin{bmatrix}{\frac {n}{7}} \end{bmatrix} }$ is divisible by $7$.
Proving ${n \choose p} \equiv \Bigl[\frac{n}{p}\Bigr] \ (\text{mod} \ p)$