How many numbers between 6000 and 7000 a divisible by 5 which can be formed with the digits 5,6,7 and 9?

Answer

To solve the problem of finding how many numbers between 6000 and 7000 can be formed using the digits 5, 6, 7, and 9 that are divisible by 5, we can follow these steps:

### Step 1: Understand the constraints
We need to form a four-digit number that:
- Lies between 6000 and 7000
- Ends with the digit 5 (to be divisible by 5)
- Starts with the digit 6 (to be between 6000 and 7000)

### Step 2: Fix the first and last digits
Since the number must start with 6 and end with 5, we can represent the number as:
\[ 6 \_ \_ 5 \]

### Step 3: Determine the middle digits
The two middle digits can be filled with any of the available digits: 5, 6, 7, or 9. Since we are allowed to repeat digits, we can choose any of these digits for both positions.

### Step 4: Calculate the combinations for the middle digits
For each of the two middle positions, we have 4 choices (5, 6, 7, or 9). Therefore, the number of combinations for the two middle digits is:
\[ 4 \times 4 = 16 \]

### Step 5: Conclusion
Thus, the total number of four-digit numbers between 6000 and 7000 that can be formed with the digits 5, 6, 7, and 9, and are divisible by 5 is:
\[ \text{Total Numbers} = 16 \]

### Final Answer
The total number of such numbers is **16**.

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