Question

The number of numbers greater than or equal to $1000$ but less than $4000$ that can be formed with $0,1,2,3,4$ so that any digit may be repeated is

• A. $374$
• B. $375$
• C. $120$
• D. $360$

Answer 1

Answer: (B)

$375$

Numbers greater than $1000$ and less than $4000$ will be of $4$ digits and will have either $1$ or $2$ or $3$ in the first place with $0$ in each of the remaining places.

After fixing first place, the second place can be filled by any of the $5$ numbers. similarly third place can be filled in $5$ ways and fourth place in $5$ ways.

Thus there will be $5\times 5\times 5=125$ ways in which $1$ will be in first place but this include $1000$ also hence there will be $124$ numbers having $1$ in first place. Similarly $125$ for each $2$ or $3$. One number will be in which $4$ in the first place i.e. $4000$. Hence the required numbers are $124+125+125+1=375$

Hence the answer is option B