The value of $\sum _{k=0}^7\left[\frac{\left(\begin{array}{c}7\\ k\end{array}\right)}{\left(\begin{array}{c}14\\ k\end{array}\right)}\sum _{r=k}^{14}\left(\begin{array}{c}r\\ k\end{array}\right)\left(\begin{array}{c}14\\ r\end{array}\right)\right]$, where $\left(\begin{array}{c}n\\ r\end{array}\right)$ denotes ${}^n{C}_r$ is

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