2009 AIME I Problem 3

A coin that comes up heads with probability p>0 and tails with probability 1-p>0 independently on each flip is flipped eight times. Suppose the probability of three heads and five tails is equal to \frac{1}{25} of the probability of five heads and three tails. Let p=\frac{m}{n}, where m and n are relatively prime positive integers. Find m+n.