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} \leq .4 for all n such that 1 \leq n \leq 9 is given to be p^{a} q^{b} r /\left(s^{c}\right), where p, q, r, and s are primes, and a, b, and c are positive integers. Find $(p+q+r+s)(a+b+c)