SOLUTION: A painter has 12 colors of paint available. When painting a house, the painter needs to choose a main color, trim color, accent color and siding color, and all of the must be diffe

Question 1115877: A painter has 12 colors of paint available. When painting a house, the painter needs to choose a main color, trim color, accent color and siding color, and all of the must be different from one another. How many ways are there for the painter to pick colors for the house ?
My work :
12P4 = 11880

Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!

12P4 if it is important which color is for which application -- that is, if for example one color is fine for a trim color but not for the main color.

But if any of the colors can be used for any application, then this is a combination instead of a permutation, so 12C4 = 495.
Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.
Your solution is correct.

In this problem, the correct solution must use permutations, not combinations.

The homes painted using different permutations of colors (even inside the same "combination") look differently ! . . .

You are right.

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On Combinations and Permutations, see the lessons
    - Introduction to Permutations
    - PROOF of the formula on the number of Permutations
    - Problems on Permutations
    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems on Combinations
    - OVERVIEW of lessons on Permutations and 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.

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