2001 Cayley Problem 12

The 6 members of an executive committee want to call a meeting. Each of them phones 6 different people, who in turn each calls 6 other people. If no one is called more than once, how many people will know about the meeting?

\textbf{(A)}\ 18\quad \textbf{(B)}\ 36\quad \textbf{(C)}\ 216\quad \textbf{(D)}\ 252\quad \textbf{(E)}\ 258

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.