Let $\displaystyle m$ be an integer with $\displaystyle m/m = p + o(1)$ for $\displaystyle 0 < p < 1$. Show $\displaystyle {n\choose{m}} = 2^{n(H+o(1))}$ where $\displaystyle H = -p \log p - (1-p) \log (1-p) $ where the logs are to the base 2.

I've tried using the binomial tail but can't get this to work...