2002 AIME II Problem 12

A basketball player has a constant probability of .4 of making any given shot, independent of previous shots. Let a_n be the ratio of shots made to shots attempted after n shots. The probability that a_{10}=.4 and a_n\le.4 for all n such that 1\le n\le9 is given to be p^aq^br/\left(s^c\right) where p, q, r, and s are primes, and a, b, and c are positive integers. Find \left(p+q+r+s\right)\left(a+b+c\right).

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.