Posted by **Tony** on Monday, December 4, 2006 at 7:40pm.

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:

XYZ

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

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