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Math Help - Number of arrangements

  1. #1
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    Number of arrangements

    Hey guys, I'm not sur how to solve this question:
    how many arrangements are there of there of two a's, one e, one i and seven x's in which no two vowels are adjacent ?
    I found that the answer would be 3! * 10! / (5! * 2!)
    is that correct ?
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  2. #2
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    Hello, sleepywalker!

    How many arrangements are there of two A's, one E, one I and seven X's
    in which no two vowels are adjacent ?
    Place the seven X's in a row, inserting spaces before, after, and between them.

    . . _ X _ X _ X _ X _ X _ X _ X _


    Now we place the 4 vowels in the 8 spaces.

    If we had 4 different vowels, there would be: . 8\cdot7\cdot6\cdot5 \:=\:1680 ways.

    Since the two A's are identical, there are: . \frac{1680}{2} \:=\:840 arrangements.

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  3. #3
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    I think this is the right answer.
    thank you so much for your time.
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