Question

If $3$ dice are rolled, then the number of possible outcomes in which at least one dice shows $5$ is

Answer 1

When a dice is rolled, there are six possible outcomes.

So, the total number of outcomes when three dice are rolled is $6\times 6\times 6=6^3$

Number of possible outcomes in which
$5$ does not appear on any dice $=5^3$

Now, the number of possible outcomes in which at least one dice shows $5$ is $=$ Total number of possible outcomes $-$ Number of possible outcomes in which
$5$ does not appear on any dice
$=6^3-5^3=91$