How many different 4 \times 4 arrays whose entries are all 1's and -1 's have the property that the sum of the entries in each row is 0 and the sum of the entries in each column is 0 ?
How many different 4 \times 4 arrays whose entries are all 1's and -1 's have the property that the sum of the entries in each row is 0 and the sum of the entries in each column is 0 ?