Question

How many $3-$digit numbers can be formed from the digits $1,2,3,4$ and $5$ assuming that
$\left(i\right)$ Repetition of the digits is allowed.
$\left(ii\right)$ Repetition of the digits is not allowed.

Answer 1

$\left(i\right)$ Forming $3-$digits numbers when repetition is allowed.
Number of ways to fill units place $=5$
Number of ways to fill tens place $=5$
Number of ways to fill hundreds place $=5$
$\therefore$ Total number of $3-$digits numbers $=5\times 5\times 5=125$

$\left(ii\right)$ Forming $3-$digits numbers when repetition is not allowed.
Number of ways to fill units place $=5$
Number of ways to fill tens place $=4$
Number of ways to fill hundreds place $=3$
$\therefore$ Total number of 3-digits numbers $=5\times 4\times 3=60$