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?

Step-by-step solution

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 .