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 with 0 in each of remaining places. After fixing 1st place, the 2ndplace 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 x 5 x 5 125 ways in which 1 will be in first place but this also
includes 1000. Hence, there will be I 24 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 + 1375.
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