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Solution


Q.

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             [2023]
1 225  
2 120  
3 125   
4 150  

Ans.

(2)

In first column, 1 can be placed in any of the 5 places = 5

In second column, 1 can be placed in any of the 4 places = 4

In third column, 1 can be placed in any of the 3 places = 3

In fourth column, 1 can be placed in any of the 2 places = 2

In fifth column, 1 can be placed in any of the 1 place = 1

Required number of ways = 5 × 4 × 3 × 2 × 1 = 120