2004 AMC 10A Problems/Problem 12

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Problem

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

$\mathrm{(A) \ } 24 \qquad \mathrm{(B) \ } 256 \qquad \mathrm{(C) \ } 768 \qquad \mathrm{(D) \ } 40,320 {2}\qquad \mathrm{(E) \ } 120,960$

Solution

A costomer can either order a condiment, or not, and there are 8 condiments. Therefore, there are $2^8=256$ ways to order the condiments.

There are also 3 choices for the meat, making a total of $256\times3=768$ possible hamburgers $\Rightarrow\mathrm{(C)}$.

See Also

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