2012 Pascal Problem 10

At the Lacsap Hospital, Emily is a doctor and Robert is a nurse. Not including Emily, there are five doctors and three nurses at the hospital. Not including Robert, there are d doctors and n nurses at the hospital. The product of d and n is

\textbf{(A)}\ 8\quad \textbf{(B)}\ 12\quad \textbf{(C)}\ 15\quad \textbf{(D)}\ 16\quad \textbf{(E)}\ 20

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 Pascal contests here.