# maximize a function which contains factorials

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 $f(k)\ge f(k+1)$.
• 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? – neticin May 21 '14 at 14:08