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Math Help - how many distinguishable words

  1. #1
    Super Member bigwave's Avatar
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    how many distinguishable words

    How many distinguishable words can be formed from the letters of the word "casserole" if each letter is used exactly once? answer is 90,720
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    If the same question were asked about the word MISSISSIPPI then the answer is \dfrac{11!}{4!\cdot 4!\cdot 2!}.

    Study that and apply to your question.
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  3. #3
    Bar0n janvdl's Avatar
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    Quote Originally Posted by bigwave View Post
    How many distinguishable words can be formed from the letters of the word "casserole" if each letter is used exactly once? answer is 90,720
    To add on to Plato's example, notice that you take the factorial of the number of letters and divide it by the factorials of the number of times a letter is repeated.
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    Super Member bigwave's Avatar
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    thanks that was it
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  5. #5
    Super Member bigwave's Avatar
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    Cool Casserole

    so then

    there are 9 letters in the word.
    (2) s (2) e

    \frac{9!}{2!2!} \rightarrow \frac{362880}{4} = 90720
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