How many numbers divisible by 5 and lying between 4000 and 5000 can be formed from the digits 4, 5, 6, 7, 8, if repetition of digits is allowed?

Explanation

To solve the problem of finding how many numbers divisible by 5 and lying between 4000 and 5000 can be formed from the digits 4, 5, 6, 7, and 8 (with repetition of digits allowed), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Range**:
- We need to form numbers that are between 4000 and 5000. This means the first digit (thousands place) can only be 4.

2. **Determine the Last Digit**:
- For a number to be divisible by 5, the last digit (units place) must be either 0 or 5. However, since we can only use the digits 4, 5, 6, 7, and 8, the only option for the last digit is 5.

3. **Choose the Middle Digits**:
- The second digit (hundreds place) and the third digit (tens place) can be any of the digits 4, 5, 6, 7, or 8. Since repetition is allowed, we have 5 choices for each of these positions.

4. **Calculate the Total Combinations**:
- The first digit is fixed as 4 (1 way).
- The second digit can be any of the 5 digits (5 ways).
- The third digit can also be any of the 5 digits (5 ways).
- The last digit is fixed as 5 (1 way).
- Therefore, the total number of combinations can be calculated as:
\[ \text{Total Numbers} = 1 \times 5 \times 5 \times 1 = 25 \]

### Final Answer:
Thus, the total number of numbers that can be formed which are divisible by 5 and lie between 4000 and 5000 is **25**.