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

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(52781) (Show Source): You can put this solution on YOUR website!
.


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

---------------

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.

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