Get Answers to all your Questions

header-bg qa

Four letters, two ' a ' and two ' b ' are filled into 16 cells of a matrix as given. It is required that each cell contains atmost one letter and each row or column cannot contain same letters. Then the number of ways the matrix can be filled is    

       
       
       
       

 

Option: 1

3600

 


Option: 2

5200


Option: 3

3960


Option: 4

4120


Answers (1)

best_answer

Selecting two rows for two ' a ' in { }^4 \mathrm{C}_2 ways. Now first ' a ' can be put in any row in 4 ways, Second ' a ' can be put in other row in 3 ways as no two a 's are in same column.

Thus two ' a ' can be filled in                                     

       
       
       
       

{ }^4 C_2 \cdot 4 \times 3=72 \text { ways. }

Similarly two ' b ' can be filled in 72 ways.
Thus two ' a ' and two ' b ' can be filled in 72^2 ways.

Now, we have to exclude the cases when

(i) both ' a ' and ' b ' are in same cell i.e., 72 ways (as after fixing ' a ' in 72 ways, ' b ' can be placed in this position)

(ii) one 'a' and  'b' are in same row or column, i.e., 72 \times16\: \text{ways}

Required number of ways =72^2-72=72 \times 16=3960

Posted by

Rishi

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE