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Question

Henry's Hamburger Heaven offers its hamburgers with the following condiments: ketchup, mustard, mayonnaise, tomato, lettuce, pickles, cheese, and onions. A customer can choose one, two, or three meat patties, and any collection of condiments. How many different kinds of hamburgers can be ordered?

Accepted Answer

A customer makes one of two choices for each condiment, to include it or not to include it. The choices are made independently, so there are 2^8 = 256 possible combinations of condiments. For each of those combinations there are three choices regarding the number of meat patties, so there are altogether (3)(256)=768 different kinds of hamburgers.