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?

#### Solution

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 = `5xx6xx6=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 =`5xx6=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`