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.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.