What you really want to show is that maximizes .
Imagine n molecules of gas confined to a rigid container divided into two chambers by a semipermeable membrane. If i molecules are in the left chamber the entropy of the system is defined by the equation
Entropy = log (n choose i)
If n is even, for what configuration of molecules will the the entropy be maximized?
(As a hint it says: Consider proving that successive terms in the sequence (n choose 0), (n choose 1), ..., (n choose n) first increase and then decrease).