How many four-digit numbers are there between 7500 and 9600 that can be formed using only the digits 3, 7, 5, 6, 8, 9 without repetition of any digits?

Sure, let's break this down:

1. The first digit can only be 7, 8, or 9 because the number must be between 7500 and 9600. So, there are 3 options for the first digit.

2. The second digit can be any of the remaining 5 digits (since we've used one for the first digit and we can't repeat digits). So, there are 5 options for the second digit.

3. The third digit can be any of the remaining 4 digits. So, there are 4 options for the third digit.

4. The fourth digit can be any of the remaining 3 digits. So, there are 3 options for the fourth digit.

To find the total number of four-digit numbers, we multiply the number of options for each digit together: 3 * 5 * 4 * 3 = 180.

So, there are 180 four-digit numbers between 7500 and 9600 that can be formed using only the digits 3, 7, 5, 6, 8, 9 without repetition of any digits.