How many numbers can be made with the help of the digits 0 ,   1 ,   2 ,   3 ,   4 ,   5 which are greater than 3000 (repetition is not allowed)

Step-by-step solution

All the 5 digit numbers and 6 digit numbers are greater than 3000 . Therefore, number of 5 digit numbers =   6 P 5 -     5 P 5 = 600 . Since the case that 0 will be at ten thousand place should be subtracted . Similarly, number of 6 digit numbers 6 !   -   5 !   =   600 . Now, the numbers of 4 digit numbers which are greater than 3000 , having 3 , 4 or 5 at first place, this can be done in 3 ways and remaining 3 digit may be filled from remaining 5 digits i.e. required number of 4