JEE MAIN - Mathematics (2023 - 24th January Evening Shift - No. 10)
The number of square matrices of order 5 with entries from the set {0, 1}, such that the sum of all the elements in each row is 1 and the sum of all the elements in each column is also 1, is :
125
150
225
120
Explanation
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$\because$ In every row and every column there would be exactly one 1 and four zeroes.
Number of matrices $={ }^{5} C_{1} \cdot{ }^{4} C_{1} \cdot{ }^{3} C_{1} \cdot{ }^{2} C_{1} \cdot{ }^{1} C_{1}=$ 120
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