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Math Help - permutation

  1. #1
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    permutation

    the number of three letter words which can be formed from the word PROPOSAL in which the middle letter is a vowel is

    how to make cases for this question

    help
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  2. #2
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    Re: permutation

    Quote Originally Posted by prasum View Post
    the number of three letter words which can be formed from the word PROPOSAL in which the middle letter is a vowel is

    how to make cases for this question

    help
    a) with letter repetition :

    2 \cdot 6^2 = 72

    b) without letter repetition :

    2 \cdot \frac{5!}{(5-2)!}=40
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  3. #3
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    Re: permutation

    40 words is not correct as I count. There are 11 sets of words beginning OA RA SA PA LA 00 RO SO PO LO AO.I count 22 words middle letter A and 31 words middle letter O
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