Question

How many numbers lying between $999$ and $10000$ can be formed with the help of the digits $0,2,3,6,7,8$, when the digits are not repeated?

• A. 100
• B. 200
• C. 300
• D. 400

Answer 1

Answer: (C)

The numbers between $999$ and $10000$ are all $4$-digit numbers.
The number of $4$ - digit numbers formed by digits
$0,2,3,6,7,8$ is ${}^6{P}_4=360$.
But here those numbers are also involved which begin from $0.$
So, we take those numbers as three-digit numbers.
Taking initial digit $0$ , the number of ways to fill remaining $3$ places from five digits
$2,3,6,7,8$ are ${}^5{P}_3=60$
So, the required numbers $=360-60=300$.