"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 __________."

Question

Accepted Answer

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In a $3\times3$ order matrix there are $9$ entries.

These nine entries are zero or one.

The sum of positive prime entries are $2, 3, 5$ or $7$.

Total possible matrices $$ = {{9!} \over {2!\,.\,7!}} + {{9!} \over {3!\,.\,6!}} + {{9!} \over {5!\,.\,4!}} + {{9!} \over {7!\,.\,2!}}$$

$= 34 + 84 + 126 + 36$

$= 282$

"

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 __________.