All the 5 digit numbers and 6 digit numbers are greater than 3000. Therefore number of 5 digit numbers

= .

{Since the case that 0 will be at ten thousand place should be omit}. 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 digit numbers are

.

Hence total required number of numbers = 600 + 600 + 180 = 1380.