2004 AMC 10A Problems/Problem 12: Difference between revisions
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==Problem== | ==Problem== | ||
Henry's Hamburger | 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> \ | <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== | ||
Think of the condiments as a set with 8 elements. There are <math>8</math> total condiments to choose from. Therefore, there are <math>2^8=256</math> ways to order the condiments. (You have two choices for each condiment- one choice is to include that condiment, and the other choice is to not include that condiment.) 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 == | ||
| Line 13: | Line 29: | ||
[[Category:Introductory Combinatorics Problems]] | [[Category:Introductory Combinatorics Problems]] | ||
{{MAA Notice}} | |||
Latest revision as of 22:27, 31 May 2025
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
Think of the condiments as a set with 8 elements. There are 
total condiments to choose from. Therefore, there are 
ways to order the condiments. (You have two choices for each condiment- one choice is to include that condiment, and the other choice is to not include that condiment.) There are also 
choices for the meat, making a total of 
possible hamburgers. 
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
Education, the Study of Everything
Video Solution
https://youtu.be/j-jNtSwTrxA?t=241 - AMBRIGGS
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 | ||
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