Q: How many integers between 1000 and 9999 have four distinct digits?
A: 1234 would be an example of a 4 digit number with distinct digits (no repeats!)
You have 9 choices for the first 1-9 (no leading zero)
You have 9 choices for the second because there are 8 left plus the zero
You have 8 choices for the third and

7 choices for the fourth digit

so 9 x 9 x 8 x 7 = 4536