Four dice are thrown simultaneously and the numbers shown on these dice are recorded in 2 × 2 matrices. The probability that such formed matrices have all different entries and are non-singular, is:

Step-by-step solution

Let, the outcomes of the four dice are a ,   b ,   c ,   d . Then, we have the matrix A = a b c d . Also, A = a b c d ⇒   A = a d - b c Now, for each of the numbers a ,   b ,   c   &   d there are 6 possibilities, hence total cases = 6 4 . For a non-singular matrix, A ≠ 0 ⇒ a d - b c ≠ 0 ⇒ a d ≠ b c Also, a ,   b ,   c ,   d are all different numbers from the set 1 ,   2 ,   3 ,   4 ,   5 ,   6 ,