Question

If four dice are rolled, find the number of possible outcomes in which atleast one die shows 2.

Answer 1

When a die is rolled number of possible outcomes is selecting an event from 6 events = ⁶C₁

When four dice are rolled number of possible outcomes = ⁶C₁ × ⁶C₁ × ⁶C₁ × ⁶C₁

When a die is rolled number of possible outcomes in which ‘2’ does not appear is selecting an event from 5 events = ⁵C₁

When four dice are rolled number of possible outcomes in which 2 does not appear = ⁵C₁ × ⁵C₁ × ⁵C₁ × ⁵C₁

Therefore the number of possible outcomes in which atleast one die shows 2

= ⁶C₁ × ⁶C₁ × ⁶C₁ × ⁶C₁ – ⁵C₁ × ⁵C₁ × ⁵C₁ × ⁵C₁

= 6 × 6 × 6 × 6 – 5 × 5 × 5 × 5

= 1296 – 625

= 671