1. The problem statement, all variables and given/known data Flip N fair coins. The distribution for different numbers of heads and tails should be peaked at N/2. When N is very large, the peak will be very high. Let x = N(head)-N/2, required to find an expression for this distribution near the peak, i.e. x<<N. 2. Relevant equations Strling Approx ln(1+x)=x for small x 3. The attempt at a solution clearly incorrect because square of (N/2)! must be smaller than the product of (N/2+x)! and (N/2-x)!, but I can't find where goes wrong.