What are the 4 digit numbers possible from 0-9 with no number repeated?

Answer 1

There are 4536 of them and I have neither the time nor the inclination to list them.

This assumes the starting digit is not 0. If 0 is allowed as the first digit, there will be 5040 such numbers.

Since each digit is used only once, this is a problem without replacement means that an outcome cannot be included more than once. In this case, the first event does affect the possibilities for the second event. These event are dependent. So the number could have any of these forms:

1_ _ _ , 2_ _ _ , 3_ _ _ , 4_ _ _ , 5_ _ _ , 6_ _ _ , 7_ _ _ , 8_ _ _ , 9_ _ _ .

There are 9 choices for the thousands digit: 1, 2, 3, 4, 5, 6, 7, 8, or 9.

After the thousands digit is chosen, 9 choices are left for the hundreds digit After the hundreds digit is chosen, 8 choices are left for the tens digit. After the tens digit is chosen, 7 choices are left for the units digit.

Then, we have (9 * 9 * 8 * 7) 4536 numbers.