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Math Help - Arranging Letters

  1. #1
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    Arranging Letters

    How many ways can the letters a,a,a,a,b,b,b,b,c,c,c (4 a's, 4 b's, 3 c's) be arranged such that 4 consecutive letters are not the same?

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  2. #2
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    Quote Originally Posted by FatherMike View Post
    How many ways can the letters a,a,a,a,b,b,b,b,c,c,c (4 a's, 4 b's, 3 c's) be arranged such that 4 consecutive letters are not the same?
    There are a total of \frac{11!}{(4!)^2(3!)} ways to arrange the string of letters
    Now count number of ways that all a's or all b's are together.
    Hint: |A|+|B|-|A\cap B| then substract.
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