Stirling's formula manipulation

Hi, I'm stuck on part of this question involving Stirling's formula. I have to show that for (they're probabilities),

if and only if

by using Stirling's approximation, which is , for large .

I know that I should be aiming to show that

I've tried rearranging it but I can't seem to get rid of the terms involving (among others).

Also, anyone who can solve this is a clever clogs, so maybe they can shed some light on this one, which seems to have defeated the SOS Math community. S.O.S. Mathematics CyberBoard :: View topic - Predictors after a simple linear regression is done

Thanks VERY much