2014 Cayley Problem 19

Two different numbers are randomly selected from the set \{-3,-1,0,2,4\} and then multiplied together. What is the probability that the product of the two numbers chosen is 0?

\textbf{(A)}\ \frac{1}{10}\quad \textbf{(B)}\ \frac{1}{5}\quad \textbf{(C)}\ \frac{3}{10}\quad \textbf{(D)}\ \frac{2}{5}\quad \textbf{(E)}\ \frac{1}{2}

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.