If three standard six-sided dice are rolled simultaneously, what is the probability that all three dice display distinct numbers?

Explanation

For all three dice to show different numbers, the first die can land on any of the 6 faces. The second die must show a different number, so it has 5 possible outcomes. The third die must differ from both previous dice, leaving 4 options. Therefore, the number of favorable outcomes is 6 × 5 × 4 = 120. Since the total number of possible outcomes when rolling three dice is 6 × 6 × 6 = 216, the probability is 120/216, which simplifies to 5/9.