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?
There are $$5$$ one-digit natural numbers out of the given digits.
For getting $$2-digit$$ natural numbers we cannot put $$0$$ at the ten's place. So, this place can be filled by any of the given five nonzero digits in $$5$$ ways.
The unit's digit can be filled by any of the given six digits in $$6$$ ways.
So, the number of $$2-digit$$ natural numbers $$= (5\times 6) = 30$$.
Similarly, to get a $$3-digit$$ number, we cannot put on at the hundred's place. So, this place can be filled in $$5$$ ways, each of the ten's and unit's places can be filled in $$6$$ ways.
$$\therefore$$ the number of $$3-digit$$ numbers $$= (5\times 6\times 6) = 180$$.
Required number of numbers $$= (5 + 30 + 180) = 215$$.