How many numbers greater than 1000, but not greater than 4000 can be formed with the digits 0, 1, 2, 3, 4 if: (i) repetition of digits is allowed? (ii) repetition of digits is not allowed?

Explanation

To solve the problem of how many numbers greater than 1000 but not greater than 4000 can be formed with the digits 0, 1, 2, 3, and 4, we will consider two cases: (i) when repetition of digits is allowed, and (ii) when repetition of digits is not allowed.

### Part (i): Repetition of digits is allowed

1. **Determine the first digit**:
- The first digit must be 1, 2, or 3 to ensure the number is greater than 1000 and not greater than 4000.
- Therefore, we have 3 choices for the first digit (1, 2, or 3).

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