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Math Help - Combinatorics Application Word Arangement

  1. #1
    Junior Member Cthul's Avatar
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    Combinatorics Application Word Arangement

    Copy of question text:
    The letters of the words 'MATHS IS THE BEST' are to be arranged in a row. The number of ways this can be done if the consonants are to be together is...
    I don't understand how to get the answer.
    I got as far as:

    \frac{2!10!4!}{?}

    The answer should be 1 209 600.
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  2. #2
    MHF Contributor

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    I disagree with the given answer.
    I think that whoever worked that out did not count the two Es.

    The number of ways to arrange the string A\boxed{C}EEI is \dfrac{5!}{2}.
    The group of consonants, \boxed{C}, can be arranged in \dfrac{10!}{2\cdot 3!\cdot 3!} ways.
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  3. #3
    MHF Contributor
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    I got the same answer as Plato.
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  4. #4
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    I completely agree with Plato . . .
    . . with his reasoning, his answer, and his suspicion.

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  5. #5
    Junior Member Cthul's Avatar
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    Whao, no wonder why. Thanks.
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