Question

How many four-digit numbers can you form from the numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9

(a) if you use each digit only once? \

I know the answer is 3,024 im just wondering how

Answer 1

3,024

Explanation:

There are digits 1, 2, 3, 4, 5, 6, 7, 8, and 9 (9 digits in total).

The first digit of 4-digit number can be selected in 9 different ways (any of given digits can be chosen), then 8 digits remain.

The second digit can be selected in 8 different ways, then 7 digits remain.

The third digit can be selected in 7 different ways, then 6 digits remain.

The fourth digit can be selected in 6 different ways.

In total, there are

`9\cdot 8\cdot 7\cdot 6=3,024`

different ways.