Numbers greater than 1000 but not greater than 4000 which can be formed with the digits 0, 1,2,3, 4 (repetition of digits is allowed) are

Numbers greater than 1000 and less than or equal to 4000 will be of 4 digits and will have either 1 (except 1000) or 2 or 3 in the 1st place. After fixing 1st place, the 2nd place can be filled by any of the 5 digits. Similarly the 3rd place can be filled up in 5 ways and 4th place can be filled up in 5 ways. Thus, there will be 5 ×5 × 5 = 125 ways in which 1 will be in first place but this also includes 1000. Hence, there will be 124 numbers having 1 in the first place. Similarly, 125 for each 2 or 3. One number will be there in which 4 will be in the first place, i.e., 4000. Hence, the required number of ways is 124 + 125 + 125 + 1 = 375