Question

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

• A. $50$
• B. $375$
• C. $450$
• D. $576$

Answer 1

Answer: (B)

$375$

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 first place with $0$ in each of remaining places.
After fixing $1$ st place, the $2$ nd place can be filled by any of the $5$ numbers.

Similarly, $3$rd place can be filled up in $5$ ways.

Thus there will be $125$ numbers in which $1$ is in first place.

But this include $1000$ also, hence there will be $124$ numbers having $1$ in the first place.

Similarly, $125$ for each $2$ or $3$.

One number will be in which $4$ is in the first place and i.e $4000$.

Hence, the required numbers of ways are $124+125+125+1=375$.