Question

How many three-digit numbers can be formed by using the digits $0,1,3,5,7$ while each digit may be repeated any number of times?

Answer 1

Given: Available digits are {$0,1,3,5,7$}

Since, the hundred's place cannot be zero,

It can be filled by any of the 4 digits ($1,3,5$ and $7$).

$\therefore$ Number of ways of filling the hundred's place $=4$
Since the digits can be repeated,

The ten's place and the unit's place can each be filled in $5$ ways.

By using the fundamental principle of multiplication, total number of numbers

$=4\times 5\times 5=100$

Hence, required three-digit numbers are $100$.