SOLUTION: Ten people are to be seated at two circular tables. One table seats six people and the other seats four. i) With these tables, how many different seating arrangements are there

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Question 1142526: Ten people are to be seated at two circular tables. One table seats six people and the other seats four.
i) With these tables, how many different seating arrangements are there for the ten people?
ii) Assuming that the seating is random, what is the probability that a particular couple will be seated at the same table?
Thank you in advance! I'm not really great at perms and comms questions. If you could include an explanation in words, I would realy appreciate it :)

Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.
(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.


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