The number of numbers divisible by 5 and lying between 40000 and 50000 that can be formed from the digits 0, 3, 4, 5, 8 and 9 ,when repetition of digits is allowed is

Options

A. 431
B. 48
C. 432
D. 84

Answer

To solve the problem of finding the number of 5-digit numbers divisible by 5 that lie between 40,000 and 50,000 using the digits 0, 3, 4, 5, 8, and 9 (with repetition allowed), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Range and Structure of the Number:**
- We need to form a 5-digit number that lies between 40,000 and 50,000.
- This means the first digit must be **4**.

2. **Determine the Last Digit for Divisibility by 5:**
- A number is divisible by 5 if its last digit is either **0** or **5**.
- Therefore, the last digit (unit place) can be either **0** or **5**. This gives us **2 options** for the last digit.

3. **Determine the Digits for the Middle Positions:**
- The second, third, and fourth digits can be any of the available digits: **0, 3, 4, 5, 8, 9**.
- Since repetition is allowed, each of these positions can have any of the **6 digits**.

4. **Calculate the Total Combinations:**
- The first digit is fixed as **4** (1 possibility).
- The second digit can be any of the 6 digits (6 possibilities).
- The third digit can also be any of the 6 digits (6 possibilities).
- The fourth digit can also be any of the 6 digits (6 possibilities).
- The last digit has 2 possibilities (0 or 5).

Therefore, the total number of combinations can be calculated as follows:
\[ \text{Total Combinations} = 1 \times 6 \times 6 \times 6 \times 2 \]

5. **Perform the Calculation:**
- First, calculate the product of the middle digits:
\[ 6 \times 6 \times 6 = 216 \]
- Now multiply by the possibilities for the last digit:
\[ 216 \times 2 = 432 \]

Thus, the total number of 5-digit numbers divisible by 5 that can be formed from the digits 0, 3, 4, 5, 8, and 9, lying between 40,000 and 50,000, is **432**.

### Final Answer:
**432**