2019 Pascal Problem 24

If p, q, r, and s are digits, how many of the 14-digit positive integers of the form 88\,663\,311\,pqr\,s48 are divisible by 792?

\textbf{(A)}\ 48\quad \textbf{(B)}\ 56\quad \textbf{(C)}\ 40\quad \textbf{(D)}\ 60\quad \textbf{(E)}\ 50

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Pascal contests here.