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Combinatorics Circular Arrangement

  1. Sep 1, 2011 #1
    1. The problem statement, all variables and given/known data
    A circular table is arranged so as to have 9 different robots occupy the table. If there are 5 different types of robots, what is the number of possible arrangements of these robots?


    2. Relevant equations



    3. The attempt at a solution

    If it wasn't a circular table, the answer would be 5^9, I suppose. But since it is circular, there would be repetitions.

    <1,2,3,4,5,6,7,8,9> is the same as <2,3,4,5,6,7,8,9,1> and so on.

    So I think I need to find the number of repetitions, and subtract it at from 5^9.

    There are 9 equivalent seating arrangements for each 'permutation'.
    for example,

    <1,2,3,4,5,6,7,8,9>
    <2,3,4,5,6,7,8,9,1>
    <3,4,5,6,7,8,9,1,2>
    <4,5,6,7,8,9,1,2,3>
    <5,6,7,8,9,1,2,3,4>
    <6,7,8,9,1,2,3,4,5>
    <7,8,9,1,2,3,4,5,6>
    <8,9,1,2,3,4,5,6,7>
    <9,1,2,3,4,5,6,7,8>

    So, is the answer 5^9/ 9 ?

    If yes, why isn't it a whole number?
     
  2. jcsd
  3. Sep 1, 2011 #2

    lanedance

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    Homework Helper

    not quite, consider the case when all 9 places have the same robot type, linking the circle doe snot make this equivalent to any other arrangements and there will not by any repetitions, so you need to be a little more careful with counting repeated sequences
     
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