SOLUTION: A catering service offers 8 ​appetizers, 9 main​ courses, and 7 desserts. A banquet committee is to select 3 ​appetizers, 5 main​ courses, and 3 desserts. How many ways can

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Question 1195580: A catering service offers 8 ​appetizers, 9 main​ courses, and 7 desserts. A banquet committee is to select 3 ​appetizers, 5 main​ courses, and 3 desserts. How many ways can this be​ done?
Answer by ikleyn(52779)   (Show Source): You can put this solution on YOUR website!
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A catering service offers 8 ​appetizers, 9 main​ courses, and 7 desserts.
A banquet committee is to select 3 ​appetizers, 5 main​ courses, and 3 desserts.
How many ways can this be​ done?
~~~~~~~~~~~~~~~~~~~~ 

There are   =  56 different ways to select 3 appetizers from 8 appetizers.

There are   = 126 different ways to select 5 main​ courses from 9 main​ courses.

There are   =  35 different ways to select desserts main​ courses from 7 desserts.


In all, there are 56*126*35 = 246960 different ways to select the entire meal of 3 components.   ANSWER

Solved.

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This problem uses  COMBINATIONS  and  Fundamental counting principle.

On these conceptions and technique,  see the lessons
    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems on Combinations
    - Fundamental counting principle problems
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic  "Combinatorics: Combinations and permutations".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.



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