How many integers greater than 999 but not greater than 4000 can be formed with the digits 0,1,2,3 and 4 if repetition of digits is allowed?
1.499
2.500
3.375
4.376
5.501
1.499
2.500
3.375
4.376
5.501
We have to find the number of 4-digit integers between 1000 and 3999 (inclusive) such that the digits are 0, 1, 2, 3 or 4 (with repetition allowed).
For the 1000 range:
first digit can be chosen in 1 way (can be only 1)
second digit can be chosen in 5 ways (0, 1, 2, 3 or 4)
third digit can be chosen in 5 ways
fourth digit can be chosen in 5 days
Number of possibilities = 125. Similarly, for 2000 and 3000 ranges, number of possibilities = 125.
Hence, total possibilities = 125*3 = 375; the answer is C.
EDIT: I always make this mistake of not comprehending the question completely. 4000 is included, hence the answer is 376 as Anurag posted below.
