Question 12
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 $a_n \le 0.4$ for all $n$ such that $1 \le n \le 9$ is given to be $\frac{p^a q^b r}{\left(s^c\right)},$ where $p,$ $q,$ $r,$ and $s$ are primes, and $a,$ $b,$ and $c$ are positive integers. Find $(p + q + r + s)(a + b + c).$