.
(i) First, you can select 6 persons from 10 people by
ways = ways = 210 ways
to seat them around the first table. Then the team for the second table will be the rest (without further choice).
Second, you can arrange 6 people around the first circular table by = 5! ways = 120 ways
(using this standard well known formula).
Third, you can arrange 4 people around the second circular table by = 3! ways = 6 ways.
Finally, the answer to the problem's question is this product
210*120*6 = 151200 ways. ANSWER
Solved.
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To expand your knowledge about combinations and permutations, look into 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
- Arranging elements of sets containing indistinguishable elements
- Persons sitting around a cicular table (*)
- Combinatoric problems for entities other than permutations and combinations
- Miscellaneous problems on permutations, combinations and other combinatoric entities
- In how many ways N distinguishable objects can be distributed among n different boxes ?
- OVERVIEW of lessons on Permutations and Combinations
in this site.
A convenient place to quickly observe these lessons from a "bird flight height" (a top view) is the last lesson in the list.
The most relevant lesson in the list is marked by (*).
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.