Difference between revisions of "2004 AMC 10A Problems/Problem 12"
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==Problem== | ==Problem== | ||
Henry's Hamburger Haven 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? | Henry's Hamburger Haven 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== | ==Solution== | ||
For each condiment, a customer may either choose to order it or not. There are <math>8</math> total condiments to choose from. Therefore, there are <math>2^8=256</math> ways to order the condiments. There are also <math>3</math> choices for the meat, making a total of <math>256\times3=768</math> possible hamburgers. <math>\boxed{\mathrm{(C)}\ 768}</math> | For each condiment, a customer may either choose to order it or not. There are <math>8</math> total condiments to choose from. Therefore, there are <math>2^8=256</math> ways to order the condiments. There are also <math>3</math> choices for the meat, making a total of <math>256\times3=768</math> possible hamburgers. <math>\boxed{\mathrm{(C)}\ 768}</math> | ||
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| + | ==Video Solution== | ||
| + | https://youtu.be/EIExyf8U7O0 | ||
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| + | Education, the Study of Everything | ||
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== See also == | == See also == | ||
Revision as of 16:44, 16 January 2021
Contents
Problem
Henry's Hamburger Haven 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?
Solution
For each condiment, a customer may either choose to order it or not. There are 
total condiments to choose from. Therefore, there are 
ways to order the condiments. There are also 
choices for the meat, making a total of 
possible hamburgers. 
Video Solution
Education, the Study of Everything
See also
| 2004 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 11 |
Followed by Problem 13 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
