How many 4 \times 4 arrays whose entries are 0 s and 1 s are there such that the row sums (the sum of the entries in each row) are 1,2,3, and 4 , in some order, and the column sums (the sum of the entries in each column) are also 1,2,3, and 4 , in some order? For example, the array
\left[\begin{array}{llll}
1 & 1 & 1 & 0 \\
0 & 1 & 1 & 0 \\
1 & 1 & 1 & 1 \\
0 & 1 & 0 & 0
\end{array}\right]
satisfies the condition.
Answer Choices
A. 144
B. 240
C. 336
D. 576
E. 624