2004 Pascal Problem 15

In the Pascal family, each child has at least 2 brothers and at least 1 sister. What is the smallest possible number of children in this family?

\textbf{(A)}\ 3\quad \textbf{(B)}\ 4\quad \textbf{(C)}\ 5\quad \textbf{(D)}\ 6\quad \textbf{(E)}\ 7

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.