A dice is rooled n times. Find the number of outcomes
(i) if 6 never appear.
(ii) if 6 appears at least once.
(iii) if only even number appears.

Explanation

When a dice is rolled n times, number of cases are `6xx6xx6`..n times`=6^(n)`.
(i) if 6 never appear, then for each trial there are five possibilities (1,2,3,4,5).
Therefore, number of outcomes for n trials will be `5xx5xx5xx`.. N times`=5^(n)`
(ii) number of cases if 6 appears at least once
=total number of cases-number of cases in which 6 never appear
`=6^(n)-5^(n)`
(iii) if only even number appear, then for each trial there are three possibilities 2,4 or 6.
So, number of outcomes for n trials will be `3xx3xx3`.. times `=3^(n)` possibilities.