Suppose I have a function $$ f(k) = \binom{500}{k} \binom{500}{1100-3k}$$ where $k$ is an integer from $200$ to $366$. How can I find the maximum analytically?
2026-03-27 17:50:27.1774633827
maximize a function which contains factorials
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Try $f(k)\ge f(k-1)$ and $f(k)\ge f(k+1)$.