Question

How many natural numbers less than 1000 can be formed from the digits 0, 1, 2, 3, 4, 5 when a digit may be repeated any number of times?

Answer 1

Since the number is less than 1000, it means that it is a three-digit number, a two-digit number or a single-digit number.
Three-digit numbers:
The hundred's place can be filled by 5 digits neglecting zero as it can't be zero.
The ten's place and the unit's place can be filled by 6 digits.
So, total number of three digit numbers = 5$\times$6$\times$6 = 180

Two-digit numbers:
The ten's place can be filled by 5 digits, except zero.

The unit's digit can be filled by 6 digits.
Total two digit numbers = 5$\times$6 = 30

Single digit numbers are 1, 2, 3, 4, 5 as 0 is not a natural number. Thus, on neglecting it, we get 5 numbers.
Total required numbers = 180 + 30 + 5 = 215