# Math Help - Question dealing with combinations

1. ## Question dealing with combinations

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).

2. What you really want to show is that $n \choose {n/2}$ maximizes $n \choose i$.