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Math Help - Combinatorics arrangements!

  1. #1
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    Combinatorics arrangements!

    for letters a,b,c,d,e,f

    -how many arrangements can there be with 'a' and 'b' next to eachother?
    (5! x 2)?

    -how many arrangements can there be with 'a' and 'b' not next to eachother?
    (6!) - (5! x 2)?

    -how many arrangements can there be with 'a' and 'b' next to eachother, but with 'a' and 'c' not next to eachother?

    thanks for the help.
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  2. #2
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    Quote Originally Posted by CSkyle View Post
    for letters a,b,c,d,e,f
    -how many arrangements can there be with 'a' and 'b' next to each other, but with 'a' and 'c' not next to eachother?
    How many ways can we have "cab"?
    How many ways can we have "bac"?
    You did the second question correctly. Can you do it again?
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  3. #3
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    Quote Originally Posted by CSkyle View Post
    for letters a,b,c,d,e,f


    -how many arrangements can there be with 'a' and 'b' next to eachother, but with 'a' and 'c' not next to eachother?

    indeed..so (5! x 2) - (3! x 2)

    thanks
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