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?


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

  • $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.