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Question from Perms and Combs unit

  1. May 14, 2007 #1
    1. The problem statement, all variables and given/known data
    Given the letters of the word ELEMENTS, how many 5 letter "words" can be found in which vowels and consonants alternate

    2. Relevant equations

    3. The attempt at a solution
    I see the need to use Cases here because the pattern can either go:

    v c v c v


    c v c v c

    So I did:

    Case 1 : vowel starts 3 5 2 4 1 = 120
    Case 2: consonant starts 5 3 4 2 3 = 360

    Add them up to get 480, however the answer says 80. What went wrong? Or was that a typo mistake?
  2. jcsd
  3. May 14, 2007 #2


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    Is there any difference between the first and last E?
  4. May 14, 2007 #3
    Don't think so.
  5. May 15, 2007 #4


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    So how many different ways are there to arrange the vowels?
  6. May 15, 2007 #5
    Nevermind, I found out what I did wrong, I forgot to devide each case by 3! for the repetitive E's.
  7. May 15, 2007 #6
    What do you mean "nevermind", that was what Nate was pointing out all along.
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