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Math Help - Permutations

  1. #1
    Junior Member Misa-Campo's Avatar
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    Permutations

    The 7 letters of the word

    G L E N E L G

    Q. What is the probability that the sequence is the same from right to left and vice-versa.

    Clue please, Thanks
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  2. #2
    Bar0n janvdl's Avatar
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    Quote Originally Posted by Misa-Campo View Post
    The 7 letters of the word

    G L E N E L G

    Q. What is the probability that the sequence is the same from right to left and vice-versa.

    Clue please, Thanks
    \frac{\boxed{GLE} \ \boxed{N} \ \boxed{ELG}}{\boxed{GLENELG}}

    The denominator can be arranged in \frac{7!}{2^3} = 630 ways.

    \boxed{GLE} can be arranged in 3! = 6 ways.


    The numerator can basically be arranged in \frac{2!}{2} = 1 way. (Because the N has to remain in the middle, thus 2!. The first and third terms, as boxed in the numerator, are the same, so we have to divide by 2.)

    Highlight text for answer.
    ****
    Thus the probability is: 6\630 = 1\105
    ****
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  3. #3
    Junior Member Misa-Campo's Avatar
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    ty

    Oh ok i get it now thanks
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