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 on digits is allowed?

(1) 499 (2)500 (3)375 (4)376 (5)501

Solution follows here:

**Solution:**
The numbers shall be between 1000 and 4000 (including the
two) and are to be formed from the given digits: 0,1,2,3 and 4.

__Case-I: Numbers starting with 1 or 2 or 3__

Digits considering from left,

1

^{st}digit can take 1 or 2 or 3 ---- 3 possibilities
As repetitions are allowed,

2

^{nd}digit can take any of the given 5 digits ---- 5 possibilities
3

^{rd}digit can take any of the given 5 digits ---- 5 possibilities
4

^{th}digit can take any of the given 5 digits ---- 5 possibilities
Applying fundamental rule, total number of possibilities =
3*5*5*5 =

**375**__Case-I: Numbers starting with 4__

The only
number under this category is 4000 ----

**1**possibility
Summing up
both the cases, total possibilities =

**376****Answer (4)**
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