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Math Help - Question About Counting Sample Points about the circle

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    Question About Counting Sample Points about the circle

    IV. The numbers of permutations of N distinct objects arranged in a circle is (n-1)!

    The Question: Why is it that in a circle the formula to be use is (n-1)! why -1?



    Spoiler:

    I did not quite understand this thread thats why I started mine.
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    Quote Originally Posted by networkmancer View Post
    IV. The numbers of permutations of N distinct objects arranged in a circle is (n-1)!

    The Question: Why is it that in a circle the formula to be use is (n-1)! why -1?
    It we are to line-up N people then it is easy to see there are N! ways to do it.

    But sitting N people around a table there is no starting (left-hand most) person.
    If we wanted to we could designate a ‘starting’ person in N ways.
    Thus there are only \frac{N!}{N}=(N-1)! different ways to do this.

    Here is another way to look at this problem.
    At a circular table with N seats, pick one to be the head of the table.
    Select one person to be seated there.
    Now there are N-1 people left.
    Starting at the right-hand side of the head-seat, there are (N-1)! ways to seat the remaining people.
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    Thanks a lot for the quick reply. Now I know . Nice forum BTW.

    +REP!
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