smc

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 $$\left[\begin{array}{cccc}1& 1& 1& 0\\ 0& 1& 1& 0\\ 1& 1& 1& 1\\ 0& 1& 0& 0\end{array}\right]$$ satisfies the condition.