2016 Pascal Problem 25

A 0 or 1 is to be placed in each of the nine 1 \times 1 squares in the 3 \times 3 grid shown so that each row contains at least one 0 and at least one 1, and each column contains at least one 0 and at least one 1. The number of ways in which this can be done is

\textbf{(A)}\ 126\quad \textbf{(B)}\ 120\quad \textbf{(C)}\ 138\quad \textbf{(D)}\ 102\quad \textbf{(E)}\ 96

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.