# How many three digit numbers can be formed by using the digits 0, 1, 3, 5, 7

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?

Solution:

Since the hundred's place cannot be zero, it can be filled by any of the 4 digits (1, 3, 5 and 7).

∴ Number of ways of filling the hundred's place = 4

Since the digits can be repeated in the number, the ten's place and the unit's place can each be filled in 5 ways.

$\therefore$ Total numbers $=4 \times 5 \times 5=100$