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

The correct option is B

$375$

Explanation for the correct option(s)

Consider the given data as,

$1000<x<4000$ and there are five digits are $0,1,2,3,4$

At unit place we can have either $1,2,3\text{or}4$

If at first place we have $1$, then rest three places can be filled by $5$ digits in the ways as expressed

$5\times 5\times 5=125$

But we need to exclude $1000$,

Hence, the total numbers is equal to $125-1=124\text{ways}$

Again, If at first place we have $2$, then rest three places can be filled by other digits by $125$ ways.

Again, If at first place we have $3$, then rest three places can be filled by other digits by $125$ ways.

We need numbers, less than $4000$, therefore, there will be only $1$ possible way

Thus, the total number formed is equal to

$124+125+125+1=375$

Hence, the correct answer is Option B.