Question

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

• A. 350
• B. 375
• C. 450
• D. 576

Answer 1

Answer: (B)

375

Answer 2

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 first place with 0 in each of remaining places.

After fixing 1^st place, the second place can be filled by any of the 5 numbers. Similarly third place can be filled up in 5 ways and 4^th 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 include 1000 also hence there will be 124 numbers having 1 in the first place. Similarly 125 for each 2 or 3. One number will be in which 4 in the first place and i.e., 4000. Hence the required numbers are 124 + 125 + 125 +1 = 375 ways.