The number of square matrices of order 5 with entries from the set 0,1, such that the sum …

Question

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

Accepted Answer

$\because$ 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

Solutions · 1