Numbers greater than $$1000$$ but not greater than $$4000$$ which can be formed with the digits $$0$$, $$1$$,$$2$$,$$3$$,$$4$$ (repetition$$ of digits is $$allowed) are

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Numbers greater than $$1000$$ and less than or equal to $$4000$$ will be of $$4$$ digits and will have either $$1$$ (except$$ $$1000) or $$2$$ or $$3$$ in the $$1st$$ place with $$0$$ in each of remaining places. After fixing $$1st$$ place, the $$2ndplace$$ can be filled by any of the $$5$$ digits. Similarly the $$3rd$$ place can be filled up in $$5$$ ways and $$4th$$ place can be filled up in $$5$$ ways. Thus, there will be $$5$$ x $$5$$ x $$5$$ $$=125$$ ways in which $$1$$ will be in first place but this alsoincludes $$1000$$. Hence, there will be I $$24$$ numbers having $$1$$ in the first place. Similarly, $$125$$ for each $$2$$ or $$3$$. one numberwill be there in which $$4$$ will be in the first place, i.e., $$4000$$. Hence, the required number of ways is $$124$$ $$+$$ $$125$$ $$+$$ $$125$$ $$+$$ $$1=375$$.

Numbers greater than 1000 but not greater than 4000 which can be formed with the digits 0, 1,2,3,4 (repetition of digits is allowed) are

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