How many natural numbers less than 1000 can be formed from the digits 0, 1, 2, 3, 4,
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?
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