how many symmetric 3x3 matrices are possible by using 5 1’s and 4 0’s?

Ans. 12 For symmetric matrix.. Set of diag should contains {1,0,1} ... And 3! Ways... Now we have two 1`s and and these 1`s can be arranged in upper triangular matrix in 3! Ways... And then other remaining 0`s can simply occupy their left positions in matrix.. hence ...3! + 3! = 12