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

(Problem)
 
(6 intermediate revisions by 5 users not shown)
Line 2: Line 2:
 
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?
  
<math> \mathrm{(A) \ } 24 \qquad \mathrm{(B) \ } 256 \qquad \mathrm{(C) \ } 768 \qquad \mathrm{(D) \ } 40,320 \qquad \mathrm{(E) \ } 120,960  </math>
+
<math> \text{(A) \ } 24 \qquad \text{(B) \ } 256 \qquad \text{(C) \ } 768 \qquad \text{(D) \ } 40,320 \qquad \text{(E) \ } 120,960  </math>
  
 
==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>
 +
 +
== 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 ==
 
== 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

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png