2018 Cayley Problem 20

Abigail chooses an integer at random from the set \{2,4,6,8,10\}. Bill chooses an integer at random from the set \{2,4,6,8,10\}. Charlie chooses an integer at random from the set \{2,4,6,8,10\}. What is the probability that the product of their three integers is *not* a power of 2?

\textbf{(A)}\ \frac{117}{125}\quad \textbf{(B)}\ \frac{2}{5}\quad \textbf{(C)}\ \frac{98}{125}\quad \textbf{(D)}\ \frac{3}{5}\quad \textbf{(E)}\ \frac{64}{125}

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.