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

Step-by-step solution

Given, A 5 × 5 matrix whose each entry is either 0 or 1 , is such that sum of entries of each column as well as each row is 1 , Taking a possible case we get, 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 Now arranging the above case we get, 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 → 5   ways → 4   ways → 3   ways → 2   ways → 1   way because if we fix 1 at first row and first column then in second row first column 1 cannot come and vice-versa