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 \(\left(p+q+r+s\right)\left(a+b+c\right)\).
(第二十届AIME2 2002 第12题)