2009 AMC 8 Problems/Problem 16

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Problem

How many $3$-digit positive integers have digits whose product equals $24$?

$\textbf{(A)}\ 12 \qquad \textbf{(B)}\ 15 \qquad \textbf{(C)}\ 18 \qquad \textbf{(D)}\ 21 \qquad \textbf{(E)}\ 24$