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Circle permutations

  1. Apr 11, 2007 #1
    1. The problem statement, all variables and given/known data
    7 people around a table, how many ways of seating if A does not want to be next to B?


    2. Relevant equations

    (n-1)!

    3. The attempt at a solution

    Well I know the number of ways to get 7 people around a table is 6! but not sure how to solve it if A does not want to be next to B.
     
  2. jcsd
  3. Apr 11, 2007 #2

    HallsofIvy

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    Seat A first anywhere at the table. There are 6 people left to seat but one of those, B, cannot be seated next to A. That means there are 5 people who could be seated on A's right side. After that choice is made, there are 4 people who could be seated on A's left side. Once you have people seated on either side of A, you can put B back into the "mix". There are now 4 people to choose the next person to seat from, then 3, then 2, then 1.
     
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