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Math Help - Gr12 Permutation Problem with a condition

  1. #1
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    Gr12 Permutation Problem with a condition

    Hi, I'm just looking for some different ways to solve this.

    How many different arrangements of the letters SPECIAL can be made using exactly 2 vowels and exactly 2 consonants?

    Thanks in advance! < 3
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  2. #2
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    Re: Gr12 Permutation Problem with a condition

    Hey Pourdo.

    Your question is a little bit ambiguous since having only 2 vowels and 2 constants means that you aren't just re-arranging the words but creating a word which has a subset of symbols.

    Are you trying to just find the number of ways of creating a new word with two vowels and two consonants?
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  3. #3
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    Re: Gr12 Permutation Problem with a condition

    Hmm sorry if it was confusing. Yes I believe it is asking how many 4 letter arrangements you can create using the letters S P E C I A L but the 4 letter arrangements must have two vowels and two consonants.

    Vowels - E I A
    Consonants - S P C L
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  4. #4
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    Re: Gr12 Permutation Problem with a condition

    Are you aware of the hyper-geometric distribution?

    Hypergeometric distribution - Wikipedia, the free encyclopedia
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  5. #5
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    Re: Gr12 Permutation Problem with a condition

    Hello, Pourdo!

    How many different arrangements of the letters SPECIAL can be made
    using exactly 2 vowels and exactly 2 consonants?
    I would solve it like this . . .


    There are 3 vowels:. \{A,E,I\}
    There are 4 consonants:. \{C,L,P,S\}

    Select 2 vowels: {3\choose2} = 3 ways.
    Select 2 consonants: {4\choose2} = 6 ways.

    Arrange the 4 letters: 4! = 24 ways.


    Therefore:. 3\cdot6\cdot24 \,=\,432 arrangements.
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  6. #6
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    Re: Gr12 Permutation Problem with a condition

    Thank you! That`s sensible.
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