I Can't Count That High...I Ran Out of Fingers and Toes!

Here is your problem of the week:

The four digits 5, 6, 7, and 8 are placed on separate cards.  How many different numbers can be formed using one or more of the cards?

Now sure, you could list out all the possibilities and then count them up; and that would certainly work just fine, though it would be a little time consuming.  Can you use your math knowledge to find the answer without listing all the possibilities?

Sincerely,
The Math Freak