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Math Help - just explain the given answer

  1. #1
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    Exclamation just explain the given answer

    hi there..

    The following questions pertain to the word SUCCESS

    a-How many different arrangements are there in which all the vowels occur before all the consonants?
    SOLUTION: Task 1: place the two vowels first. We have 2 choices.
    Task 2: place the “five” remaining consonants next. We have 5!/(2! 3!) ways, by virtue of the same formula. By the Fundamental Counting Principle we end up with (2) 5!/(2! 3!) arrangements, that is, 20.

    *i cant understand where did the (2) come from

    b-How many different arrangements are there in which all the vowels occur before all the consonants?
    (size of A) / (size of any class) = 420 ÷ 10 = 42
    didnt know how to approach this type of questions



    thanks
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  2. #2
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    Quote Originally Posted by alex83 View Post
    The following questions pertain to the word SUCCESS

    a-How many different arrangements are there in which all the vowels occur before all the consonants?
    SOLUTION: Task 1: place the two vowels first. We have 2 choices.
    Task 2: place the “five” remaining consonants next. We have 5!/(2! 3!) ways, by virtue of the same formula. By the Fundamental Counting Principle we end up with (2) 5!/(2! 3!) arrangements, that is, 20
    *[COLOR=Red]i cant understand where did the (2) come from
    "UE" OR "EU" that is TWO ways.
    -----
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