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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?

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Try $f(k)\ge f(k-1)$ and $f(k)\ge f(k+1)$.

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  • $\begingroup$ Can't believe that actually simplifies to a linear inequation! $\endgroup$ – user88595 May 21 '14 at 12:48
  • $\begingroup$ Just a condition for maxima. $\endgroup$ – evil999man May 21 '14 at 12:49
  • $\begingroup$ That's awesome, +1! $\endgroup$ – Inactive - avoiding CoC May 21 '14 at 12:51
  • $\begingroup$ Thanks for this but when you try to solve $f(k) \geq f(k-1)$ you get an equation with 4th degree. Is there a simpler way of doing it? $\endgroup$ – neticin May 21 '14 at 14:08
  • $\begingroup$ @neticin A cubic. I can't think of a better way. What is the source of this problem? $\endgroup$ – evil999man May 21 '14 at 14:26

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