Difference between revisions of "2004 AMC 10A Problems/Problem 12"
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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? | 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? | ||
| − | <math> \mathrm{(A) \ } 24 \qquad \mathrm{(B) \ } 256 \qquad \mathrm{(C) \ } 768 \qquad \mathrm{(D) \ } 40,320 | + | <math> \mathrm{(A) \ } 24 \qquad \mathrm{(B) \ } 256 \qquad \mathrm{(C) \ } 768 \qquad \mathrm{(D) \ } 40,320 \qquad \mathrm{(E) \ } 120,960 </math> |
==Solution== | ==Solution== | ||
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*[[2004 AMC 10A Problems/Problem 13|Next Problem]] | *[[2004 AMC 10A Problems/Problem 13|Next Problem]] | ||
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| + | [[Category:Introductory Combinatorics Problems]] | ||
Revision as of 12:10, 5 November 2006
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?
Solution
A costomer can either order a condiment, or not, and there are 8 condiments. Therefore, there are 
ways to order the condiments.
There are also 3 choices for the meat, making a total of 
possible hamburgers 
.
