2009 Cayley Problem 19

How many integers n are there with the property that the product of the digits of n is 0, where 5000 \leq n \leq 6000?

\textbf{(A)}\ 332\quad \textbf{(B)}\ 270\quad \textbf{(C)}\ 301\quad \textbf{(D)}\ 272\quad \textbf{(E)}\ 299

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 Cayley contests here.