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Math Help - Permutation

  1. #1
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    Calculate the number of ways to arrange all the letters of the word 'LONGITUDES' if all the vowels are separated from each other. Thanks a lot for your help!
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  2. #2
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    Quote Originally Posted by cyt91 View Post
    Calculate the number of ways to arrange all the letters of the word 'LONGITUDES' if all the vowels are separated from each other. Thanks a lot for your help!
    hi

    it has to be arranged like this .

    _L_N_G_T_D_S_

    where the 4 vowels will fill up any of the empty blanks and LNGTDS itself can be arranged in 6! ways.

    so the answer would be 7C4 x 6!
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  3. #3
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    Thanks a lot. Though I think it's 7P4 x 6!. Anyway,you showed me the way. Many thanks.
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  4. #4
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    \binom{7}{4}4!6!=7P4
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