How many different three-digit numbers can be written using the digits 4, 5, 6, and 7? Use each digit only once in a number.

Is the answer---24 different 3-digit numbers? I did this the long way--Is there a short equation to use for this?
Thank you!

You have four digits:
The first choice can be any of the 4, there are four ways to get it.
The second choice can be any of three, there are three ways..
and so on.

Answer: 4*3*2

The 3 digit numbers are of the form:


For X you have 4 choices. Once you have chosen X you have 3 choices left for Y and then there are 2 choices for Z.

The total number of choices is then 4*3*2 = 24

Yes, you are correct! The short equation to determine the number of different three-digit numbers is indeed 4*3*2.

To explain further, we need to consider the position of each digit in the three-digit number.

For the first digit (X), you have 4 choices (4, 5, 6, or 7). Once you have chosen the first digit, there are 3 remaining choices for the second digit (Y). Finally, for the third digit (Z), there are 2 choices left after choosing the first two digits.

To calculate the total number of different three-digit numbers, you multiply the number of choices for each digit together: 4*3*2 = 24.

So, there are 24 different three-digit numbers that can be formed using the digits 4, 5, 6, and 7, ensuring that each digit is used only once in a number.