JEE MAIN - Mathematics (2022 - 29th July Morning Shift - No. 20)
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
282
Explanation
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 $$ = {{9!} \over {2!\,.\,7!}} + {{9!} \over {3!\,.\,6!}} + {{9!} \over {5!\,.\,4!}} + {{9!} \over {7!\,.\,2!}}$$
$$ = 34 + 84 + 126 + 36$$
$$ = 282$$
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