Expert: Paul Klarreich - 3/2/2006

Question
there are 8 different toppings that you can choose to include or leave off of a hamburger. You can choose as few or as many toppings as you likes. How many different options do he have when building his hamburger?

I tried 2^8 but its not working

Answer
Hi, Kevin,
You wrote:
Subject:  combination problem
Question:  there are 8 different toppings that you can choose to include or leave off of a hamburger. You can choose as few or as many toppings as you like. How many different options do you have when building a hamburger?

I tried 2^8 but its not working
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I don't see why -- 2^8 looks OK to me.  Since there are no restrictions on the number, you are choosing a subset of the set of 8 toppings.  The number of such subsets, not limited by size, is the 'power set', and it has 2^n, in this case 2^8, elements.

The alternative solution just assumes that for each of the 8 toppings you either include it or exclude it, so you have 8 two-way choices.  Again you have 2^8 ways of making them.

So perhaps there was some other restriction you overlooked.