2017 Pascal Problem 25

Sam thinks of a 5-digit number. Sam's friend Sally tries to guess his number. Sam writes the number of matching digits beside each of Sally's guesses. A digit is considered "matching" when it is the correct digit in the correct position.

\begin{array}{c|c} \text{Guess} & \text{Number of Matching Digits} \\ \hline 51545 & 2 \\ 21531 & 1 \\ 71794 & 0 \\ 59135 & 1 \\ 58342 & 2 \\ 37348 & 2 \\ 71744 & 1 \end{array}

What is the sum of all of the possibilities for Sam's number?

\textbf{(A)}\ 525\,768\quad \textbf{(B)}\ 527\,658\quad \textbf{(C)}\ 527\,568\quad \textbf{(D)}\ 526\,578\quad \textbf{(E)}\ 526\,758

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.