2019 Fermat Problem 18

How many 7-digit positive integers are made up of the digits 0 and 1 only, and are divisible by 6?

\textbf{(A)}\ 16\quad \textbf{(B)}\ 11\quad \textbf{(C)}\ 21\quad \textbf{(D)}\ 10\quad \textbf{(E)}\ 33

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 Fermat contests here.