Question

The number of matrices of order $3\times 3$, whose entries are either 0 or 1 and the sum of all the entries is a prime number, is

Answer 1

Answer: 282

$A=\left|\begin{array}{ccc}a11& a12& a13\\ a21& a22& a23\\ a31& a32& a33\end{array}\right|a_{ij}\in \left\{0,1\right\}$
$\sum a_{ij}=2,3,5,7$
$\text{ Total matrix }={}^9{C}_2+{}^9{C}_3+{}^9{C}_5+{}^9{C}_7$
$=282$