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Math Help - Order of items around a circle

  1. #1
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    Order of items around a circle

    I am trying to figure out how many ways 20 beads can be placed around a necklace, but i'm not really sure where to start.

    Could someone give me a hint on this?

    my thought is that it is 20! / 20
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  2. #2
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    If we arrange twenty persons around a circular table, that can be done in
    19! ways.

    But with beads on a necklace we can view it from two sides.
    That is to say if we had three beads: red, green, & blue.
    There would be only one necklace.

    \begin{array}{*{20}c}<br />
   {} & {red} & {}  \\<br />
   {blue} & {} & {green}  \\ \end{array} is the same as \begin{array}{*{20}c}<br />
   {} & {red} & {}  \\<br />
   {green} & {} & {blue}  \\ \end{array}
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