The corner points of the feasible region determined by x + y ≤ 8, 2x + y ≥ 8, x ≥ 0, y ≥ 0 are A(0, 8), B(4, 0), and C(8, 0). If the objective function Z = ax + by has its maximum value on the line segment AB, then the relation between a and b is:
A die is rolled thrice. What is the probability of getting a number greater than 4
in the first and second throw of the dice, and a number less than 4 in the third throw?