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Q.
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
E.
None of the above
View Answer
Correct choice: B
Explanation:
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=125ways 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.
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