Q194 / 270 · NDA 2026 (Phase 1) · Mathematics
How many numbers greater than $1000$ can be formed using the digits $0$, $1$, $2$ and $3$ (repetition of digits is not allowed) ?
- A$24$
- Correct answerB$18$
- C$15$
- D$12$
Solution
To form a number greater than $1000$ using the digits $0, 1, 2, 3$ without repetition, the number must be a $4$-digit number.
The thousands place cannot be $0$, so it can be filled in $3$ ways (using $1, 2,$ or $3$).
The remaining $3$ places can be filled with the remaining $3$ digits in $3!$ ways.
Total number of such numbers $= 3 \times 3! = 3 \times 6 = 18$.
Answer: $18$
The thousands place cannot be $0$, so it can be filled in $3$ ways (using $1, 2,$ or $3$).
The remaining $3$ places can be filled with the remaining $3$ digits in $3!$ ways.
Total number of such numbers $= 3 \times 3! = 3 \times 6 = 18$.
Answer: $18$
Hence, the correct answer is option: 'B'.