Your mind will explode #4

Discrete Mathematics Level pending

A basketball player has a constant probability of \(0.4\) 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 \(a_{10} = 0.4\) and \(a_n \leq 0.4\) for all \(n\) such that \(1\le n\le9\) is given to be \(\dfrac{p^aq^br}{s^c}\) where \(p\), \(q\), \(r\), and \(s\) are primes, and \(a\), \(b\), and \(c\) are positive integers.

Submit the value of \(\left(p+q+r+s\right)\left(a+b+c\right)\) as your answer.

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