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. $350$
• B. $375$
• C. $450$
• D. $576$

Answer 1

Answer: (B)

$375$

Number 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 $1^{st}$ place with $0$ in each of remaining places.

After fixing $1^{st}$ place, the $2^{nd}$ place can be filled by any of the $5$ digits.

Similarly the $3^{rd}$ place can be filled up in $5$ ways and $4^{th}$ place can be filled up in $5$ ways.

Thus, there will be $5\times 5\times 5=125$ ways in which $1$ will be in first place but this also includes $1000$.
Hence, there will be $124$ numbers having $1$ in the first place.
Similarly, $125$ for each $2$ or $3$.

One number will be there in which $4$ will be in the first place. i.e., $4000$.

Hence, the required number of ways is $124+125+125+1=375$.