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The problem asks how many distinguishable permutations/arrangements are possible of 8 flags, of which 4 are white, 2 are red and 2 are blue.
The total number of permutations of 8 flags is 8!.
Of them, the number of distinguishable arrangements /(signals) is = 420.
Solved.
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On permutations, see the lessons
- Introduction to Permutations
- PROOF of the formula on the number of Permutations
- Problems on Permutations
On distinguishable permutations, see the lesson
- Arranging elements of sets containing indistinguishable elements
- 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.