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

$A=\left[\begin{array}{ccc}{a}_{11}& a_{12}& a_{13}\\ a_{21}& a_{22}& a_{23}\\ a_{31}& a_{32}& a_{33}\end{array}\right]a_{ij}\in \{0,1\}$
$\sum a_{ij}=2,3,5,7$
Total matrix $={}^9{C}_2+{}^9{C}_3+{}^9{C}_5+{}^9{C}_7$
$=282$