SOLUTION: "There are 12 food items on a dinner table. Suppose a person is allowed to get only 8 food items. How many ways can the person choose?" I am kind of confused if this is a permut

Algebra ->  Permutations -> SOLUTION: "There are 12 food items on a dinner table. Suppose a person is allowed to get only 8 food items. How many ways can the person choose?" I am kind of confused if this is a permut      Log On


   

Question 1179508: "There are 12 food items on a dinner table. Suppose a person is allowed to get only 8 food items. How many ways can the person choose?"
I am kind of confused if this is a permutation or a combination problem - my first answer is in combination: 12C8 = 495. But I am not sure if this is correct.
It would mean a lot if someone could correct me or confirm this, I have trouble determining if a problem is in permutation or combination. Thank you!
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.

The rule and the way to distinct between permutations and combinations is  THIS:

        - if the order in selections  DOES  matter,  then the selections are  PERMUTATIONS.

        - if the order in selections  DOES  NOT  matter,  then the selections are  COMBINATIONS.



Regarding this problem,  is something in the text or in the context,  that makes the order important ?



I do not see any signs of it  NEITHER  in the text,  NOR  in the context.

So,  I conclude that the problem is about  COMBINATIONS.


----------------

On permutations and combinations,  see introductory lessons

    - Introduction to Permutations
    - PROOF of the formula on the number of Permutations
    - Simple and simplest problems on permutations
    - Special type permutations problems

    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems on Combinations

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.