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Math Help - Combinatorics: permutations help

  1. #1
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    Combinatorics: permutations help

    Hi, I need help with the question;
    Determine the number of ways of arranging the letters in the word handle if:
    a) the first letter must and consonant
    b) the second and fifth letter must be a vowel

    Thanks
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  2. #2
    Junior Member
    Joined
    Nov 2008
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    a)First letter a consonant, did I read well?
    Suppose you put the H in the first place; you get
    H _ _ _ _ _ that means you have 5 letters to put in 5 places; thatīs a permutation of 5 elements: 5!
    Doing the same with the other consonants it means that you have 4.5!=480 ways.

    b) _ vowel _ _ vowel _

    and you only have two possibilities:
    _ A _ _ E _ (permutation of 4 elements)
    or
    _ E _ _ A _ (permutation of 4 elements)

    that leads to 2.4!=48

    Iīm assuming there are no repeated letters on an arrangement.
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  3. #3
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    Thanks for help, you explained it well.
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