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Math Help - permutation question

  1. #1
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    Nov 2009
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    permutation question

    In how many ways can 5 different trees be planted in a circle.
    The answer is 24. I would think that it should be 5! but instead it is 4!? Does anyone understand this problem?
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  2. #2
    Senior Member
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    Nov 2009
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    You can rotate a circle...

    You can rotate a circle without changing it's essential layout. Take a clock for example. If we rotate the clock so that the "1" is straight up, all the other numbers are out of position. However we think the arrangement of numbers is still the same.

    For your problem, you have to arbitrarily place one tree at a fixed spot on the circle. Then you have to count the positions to put the other 4 trees, giving you 4!
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