# Three Dice Are Rolled. Find the Number of Possible Outcomes in Which at Least One Die Shows 5 ? - Mathematics

Three dice are rolled. Find the number of possible outcomes in which at least one die shows 5 ?

#### Solution

Required number of possible outcomes = (Total number of outcomes - Number of possible outcomes in which 5 does not appear on any of the dice.)
Total number of outcomes when a single dice is rolled = 6
∴ Total number of outcomes when two dice are rolled =6xx6

Similarly, total number of outcomes when three dice are rolled =6xx6xx6=216

Number of possible outcomes in which 5 does not appear on any dice =5xx5xx5=125

∴ Required number of possible outcomes =216-125=91

Concept: Permutations
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 16 Permutations
Exercise 16.2 | Q 43 | Page 16