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Math Help - How many permutations are there?

  1. #1
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    Smile How many permutations are there?

    The English alphabet has 26 letters, 5 of these are vowels.
    How many permutations of English letters are there in which all vowels are in consecutive places?

    My answer:
    There are C(26,5) + C(26,26-5) = C(26,5) + C(26,21) = 2C(26,5) = 265780 = 131560 permutations.

    Is my answer correct? If not, please explain how one should address this problem. Thanks.
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  2. #2
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    Quote Originally Posted by feyomi View Post
    The English alphabet has 26 letters, 5 of these are vowels.
    How many permutations of English letters are there in which all vowels are in consecutive places?

    My answer:
    There are C(26,5) + C(26,26-5) = C(26,5) + C(26,21) = 2C(26,5) = 265780 = 131560 permutations.
    No that is not correct.
    Here is the answer in the back of the book: (5!)(22!).
    You tell us why.
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  3. #3
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    Quote Originally Posted by Plato View Post
    No that is not correct.
    Here is the answer in the back of the book: (5!)(22!).
    You tell us why.

    Ah right okay, so there are 5! ways of arranging the vowels and 21! ways of arranging the consonants, and by rule of product, the answer is 5!21! ?

    Did you mean 21 instead of 22? If not, I'm not sure where the 22 comes from
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  4. #4
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    Quote Originally Posted by feyomi View Post
    Ah right okay, so there are 5! ways of arranging the vowels and 21! ways of arranging the consonants, and by rule of product, the answer is 5!21! ?

    Did you mean 21 instead of 22? If not, I'm not sure where the 22 comes from
    The five vowels form one block. With the twenty-one consonants that gives us 22 blocks to arrange.
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