Difference between revisions of "2004 AMC 10A Problems/Problem 12"

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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>
  
== Video Solution ==
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== Video Solution by OmegaLearn ==
 
https://youtu.be/0W3VmFp55cM?t=373
 
https://youtu.be/0W3VmFp55cM?t=373
  
 
~ pi_is_3.14
 
~ pi_is_3.14
 +
 +
== Video Solution ==
 +
https://youtu.be/3MiGotKnC_U?t=950
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~ ThePuzzlr
  
 
==Video Solution==
 
==Video Solution==
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Education, the Study of Everything
 
Education, the Study of Everything
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==Video Solution==
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https://youtu.be/j-jNtSwTrxA?t=241 - AMBRIGGS
  
 
== See also ==
 
== See also ==

Latest revision as of 00:25, 21 November 2022

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?

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

Solution

For each condiment, a customer may either choose to order it or not. There are $8$ total condiments to choose from. 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. $\boxed{\mathrm{(C)}\ 768}$

Video Solution by OmegaLearn

https://youtu.be/0W3VmFp55cM?t=373

~ pi_is_3.14

Video Solution

https://youtu.be/3MiGotKnC_U?t=950

~ ThePuzzlr

Video Solution

https://youtu.be/EIExyf8U7O0

Education, the Study of Everything

Video Solution

https://youtu.be/j-jNtSwTrxA?t=241 - AMBRIGGS

See also

2004 AMC 10A (ProblemsAnswer KeyResources)
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

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