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Math Help - Permutations with different numbers of objects

  1. #1
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    Permutations with different numbers of objects

    Hi there.

    I am trying to find the number of different permutations for the following problem:

    Box
    Box 1 Red Blue Green
    Box 2 Red Blue Green
    Box 3 Red Blue Green
    Box 4 Red Blue Green
    Box 5 Red Blue n/a
    Box 6 Red Blue n/a
    Box 7 Red Blue n/a


    I have seven boxes.Three of the boxes (box 5,6&7) can be either red or blue. Four of the boxes (box 1,2,3&4) can be either red, blue or green. How do I find out the number of permutations of all seven boxes?

    i.e
    What is the value of n?
    Combination Box 1 Box 2 Box 3 Box 4 Box 5 Box 6 Box 7
    Combination 1 R R R R R R R
    Combination 2 R R R R R R B
    Combination 3 R R R R R B R
    ..... ... ... ... ... ... ... ...
    Combination n


    Thanks
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  2. #2
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    Re: Permutations with different numbers of objects

    Can you answer the following (easier, but analogous) question? I have 3 different pairs of shirts and 2 different pairs of pants. How many different outfits can I make? How can this help you answer your question?
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  3. #3
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    Re: Permutations with different numbers of objects

    hi,

    Thanks for responding.
    "I have 3 different pairs of shirts and 2 different pairs of pants. How many different outfits can I make?"

    I believe that you could make 6 different outfits.

    Im not sure how this helps me?
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  4. #4
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    Re: Permutations with different numbers of objects

    You have three choices for Box 1, 2, 3, and 4 and two choices for 5, 6, and 7. All are independent choices, therefore, it is similar to choosing outfits, just as you calculated (i.e. the product of choices).
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  5. #5
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    Re: Permutations with different numbers of objects

    I understand now.

    So
    n= (3^4)*(2^3)
    = 648

    If so, thanks!
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  6. #6
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    Re: Permutations with different numbers of objects

    Quote Originally Posted by qwertyasd View Post
    I understand now.

    So
    n= (3^4)*(2^3)
    = 648

    If so, thanks!
    That's correct.
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