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Math Help - combinations

  1. #1
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    combinations

    Your making a necklace with 4 red peices and 4 yellow peices. How many different combination of necklaces can you make?

    is 2^8 correct.
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  2. #2
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    Re: necklace

    2^8 is not correct.

    Here's why:
    2^8 assumes a necklace like:
    RYRYRYRY
    is different than a necklace like:
    YRYRYRYR

    You need to reflect this in your counting to obtain the correct (i.e. lower) answer.
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  3. #3
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    Hello, harold3331!

    This is a very tricky problem . . .


    You're making a necklace with 4 red pieces and 4 yellow pieces.
    How many different combination of necklaces can you make?

    is 2^8 correct? . . . . no

    Your answer assumes there are at least eight of each color
    . . and includes all the combinations from RRRRRRRR\text{ to }YYYYYYYY.


    Even worse, this is a necklace . . . a circular arrangement.
    So that, for example: . RRRRYYYY \:=\:RRYYYYRR

    . . That is: . \begin{array}{cccc}& R\;R \\ Y & & R \\ Y & & R \\ & Y\;Y \end{array}\quad= . . \begin{array}{ccc}& R\;R \\ R & & Y \\ R & & Y \\ & Y\;Y \end{array}



    There is one more "trap" in a Necklace Problem, overlooked by the best of us.

    This is similar to seating 4 men and 4 women around a circilar table,
    . . except a necklace can be "flipped over".

    So that: . \begin{array}{ccc} & R:R \\ Y &: & R \\ Y &:& Y \\ & Y:R\end{array} . . = \quad \begin{array}{ccc}& R:R \\ R &:& Y \\ Y &:& Y \\ & R:Y\end{array}


    Care to try again?

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