The number of matrices of order 3 × 3 , whose entries are either 0 or 1 and the sum of all the entries is a prime number, is _______.

Step-by-step solution

Let the matrix be a b c d e f g h i Since the elements can be either of 0   or   1 , so a + b + c + d + e + f + g + h + i = 2 / 3 / 5 / 7 For sum as 2 , the number of cases will be 9 ! 2 ! 7 ! = 36 For sum as 3 , the number of cases will be 9 ! 3 ! 6 ! = 84 For sum as 5 , the number of cases will be 9 ! 5 ! 4 ! = 126 For sum as 7 , the number of cases will be 9 ! 2 ! 7 ! = 36 Total required matrix will be 282