2002 Gauss 7 Problem 25

Each of the integers 226 and 318 have digits whose product is 24. How many three-digit positive integers have digits whose product is 24?

\textbf{(A)}\ 4\quad \textbf{(B)}\ 18\quad \textbf{(C)}\ 24\quad \textbf{(D)}\ 12\quad \textbf{(E)}\ 21

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 Gauss contests here.