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