World Tour Thailand6

\[\displaystyle \sum _{k=84}^{8000}\left(\begin{array}{c}k\\ 84\end{array}\right)\left(\begin{array}{c}8084-k\\ 84\end{array}\right) = \left(\begin{array}{c}n \\ r\end{array}\right)\]

If \(n\) and \(r\) are positive integers, find the lowest possible value of \(n+r\).

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