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

• A. 225
• B. 120
• C. 125
• D. 150

Answer 1

Answer: (B)

In each row and each column exactly one is to be placed -
$\therefore$ No. of such materials $=5\times 4\times 3\times 2\times 1=120$
Alternate :

Step-1 : Select any 1 place for 1 's in row 1. Automatically some column will get filled with 0 's.
Step-2 : From next now select 1 place for 1's. Automatically some column will get filled with 0 's. $\Rightarrow$ Each time one less place will be available for putting 1's.
Repeat step-2 till last row.
Req. ways $=5\times 4\times 3\times 2\times 1=120$