.
(a) In (4-1)! = 3! = 1*2*3 = 6 different ways.
In this problem, special type of permutations is considered: CIRCULAR permutations - - - NOT LINEAR permutations.
Number " 5 " in your post is IRRELEVANT.
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To see many other similar (and different) solved problems on CIRCULAR PERMUTATIONS, look into the lesson
- Persons sitting around a cicular table
in this site, and learn the subject from there.
Also, you have this free of charge online textbook in ALGEBRA-II in this site
- ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lesson is 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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