The number of matrices of order 3×3, whose entries are either 0 or 1 and the sum of all the entries is a prime number, is \_\_\_\_\_\_\_\_.
Answer: 282
Solutions · 1
Official solution
There are 9 entries; possible prime sums: 2,3,5,7.
\[\binom92+\binom93+\binom95+\binom97=36+84+126+36=282.\]