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2004 AMC 10A Problem 12

Problem 12 of 25IntermediateCombinatorics

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?

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Solution

Each of the 88 condiments is independently in or out, giving 28=2562^8 = 256 condiment combinations. For each of these there are 33 choices of patty count, so the number of hamburgers is 3×256=768. 3 \times 256 = 768. Thus, the correct answer is C.
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Tagged: multiplication principle · subsets

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