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Math Help - Permutation of theory

  1. #1
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    Permutation of theory

    Each permutation of the letters in THEORY is written on a slip of paper and tossed into a bowl. One slip is drawn at random, what is the probability that the letter T willappear in the last position?
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  2. #2
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    Quote Originally Posted by Jigglypuff View Post
    Each permutation of the letters in THEORY is written on a slip of paper and tossed into a bowl. One slip is drawn at random, what is the probability that the letter T willappear in the last position?
    THEORY... Six letters.
    Only one can come last at any given time.
    There's a one in six chance that this will be 'T'.
    So: 1/6.
    That's probably the simplest way of looking at it...

    You could also say that you had:
    5/6 * 4/5 * 3/4 * 2/3 * 1/2 * 1/1 = 1/6.

    I think...
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  3. #3
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    Hello, Jigglypuff!

    Yet another approach . . .


    Each permutation of the letters in THEORY is written on a slip of paper
    and tossed into a bowl. One slip is drawn at random.
    What is the probability that the letter T will appear in the last position?
    There are 6! = 720 permutations of the six letters.
    . . Hence, there are 720 slips of paper in the bowl.


    If T is last: . \_\:\_\:\_\:\_\:\_\:T
    . . the other 5 letters can be arranged in 5! = 120 ways.
    Hence, there are 120 slips with T in the last position.


    Therefore: . P(\text{ T is last }) \;=\;\frac{120}{720} \;=\;\boxed{\frac{1}{6}}

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