SOLUTION: Find the number of ways that 9 persons can arrange themselves: a) around a table where two of them sit beside each other; b) around a table (no restrictions); c) in a row of

Algebra ->  Permutations -> SOLUTION: Find the number of ways that 9 persons can arrange themselves: a) around a table where two of them sit beside each other; b) around a table (no restrictions); c) in a row of      Log On


   



Question 1184483: Find the number of ways that 9 persons can arrange themselves:
a) around a table where two of them sit beside each other;
b) around a table (no restrictions);
c) in a row of 9 chairs.

Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
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a)  around a table where two of them sit beside each other;

       2*(9-2)! = 2*7! = 2*5040 = 10080.    ANSWER



b)  around a table (no restrictions);

        (9-1)! = 8! = 40320.      ANSWER



c)  in a row of 9 chairs.

       9! = 362880.      ANSWER

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On Permutations,  see introductory lessons
    - Introduction to Permutations
    - PROOF of the formula on the number of Permutations
    - Simple and simplest problems on permutations
    - Persons sitting around a circular table
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.