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

In a $3\times 3$ order matrix there are $9$ entries.

These nine entries are zeros or ones.

The sum of all possible entries can be $2,3,5$ or $7$.

Total possible matrices $=\frac{9!}{2!\cdot 7!}+\frac{9!}{3!\cdot 6!}+\frac{9!}{5!\cdot 4!}+\frac{9!}{7!\cdot 2!}$

$=36+84+126+36$

$=282$