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Math Help - simple permutations

  1. #1
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    simple permutations

    From the word, FORMULA, five letters are selected at random and arranged in a straight line. What is the probability that if one such arrangement is selected at random that the three vowels are together?

    THANKS!!!
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  2. #2
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    Quote Originally Posted by differentiate View Post
    From the word, FORMULA, five letters are selected at random and arranged in a straight line. What is the probability that if one such arrangement is selected at random that the three vowels are together?

    THANKS!!!
    There are 7! arrangements of FORMULA

    If the 3 vowels are together, take them as a group.
    There are 5! arrangements of the group with the other 4 letters.
    However the group itself can be arranged in 3! ways.
    That's 3!4! arrangements with the vowels together.

    If 5 of the 7 are chosen, there are 7p_5 arrangements,
    and there are 3! arrangements with the 3 taken as a group,
    giving 3!3! arrangements that contain all 3 vowels.

    The probability can be calculated then.
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