Expert: Steve Holleran - 5/28/2007

Question
I have a book that features 100 different exercises. And each 'workout' let's you choose only 8 of the exercises (it's a flip-chart type book). And each of these exercises CAN repeat.

So one workout can be
1st Exercise: pushups
2nd Exercise: situps
3rd Exercise: pushups
4th Exercise: running

How many total workout combinations are there and how did you figure it out?

Thank you!

Answer
Hi Ryan,

I think I understand your question, but I'm not sure you're going to like the answer.  All you really have to use is the Fundamental Counting Principle:

When you go to pick the first exercise, you basically have 100 choices.  Then, since you can repeat exercises, for each of the additional seven exercises, you also have the same 100 choices.  Since you have 8 selections, and 100 choices for each selection, you then will have :

100 * 100 * 100 * ... * 100 (8 times)

or 100^8 or 10^16 workouts.

Of course, you have to realize that under these conditions, all 8 exercises COULD be pushups, or all 8 situps, etc.

I hope I've answered your question

Steve Holleran