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Math Help - Probability Question

  1. #1
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    Wink Probability Question

    A group of eight is to be chosen at random from eight men and six women.
    What is the probability that
    i. the group contains the same number of men and women?
    ii. the group contains at most one woman?
    iii. the group contains the oldest person but not the youngest person?
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  2. #2
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    there are no new concepts here from what you posted in

    http://www.mathhelpforum.com/math-he...ability-q.html

    If you are stuck please say exactly where, dont post your entire assignment on the forum in different threads
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  3. #3
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    Well heres what I did
    (8 choose 4) x (6 choose 4) = 70 x 15 = 1050
    (14 choose 8) = 3003

    so the probability = 1050/3003.
    I dont know if thats right though
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  4. #4
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    Quote Originally Posted by Detanon View Post
    Well heres what I did
    (8 choose 4) x (6 choose 4) = 70 x 15 = 1050
    (14 choose 8) = 3003

    so the probability = 1050/3003.
    I dont know if thats right though
    Yes, that's fine since any group of 4 men can go with any group of 4 women,
    which is why the selections are multiplied.

    (ii)

    At most 1 woman is 1 woman or no women,
    which means 1 woman and 7 men or all 8 men.

    P=\frac{\binom{8}{7}\binom{6}{1}+\binom{8}{8}\bino  m{6}{0}}{\binom{14}{8}}

    (iii)

    If the group contains the oldest person and excludes the youngest person,
    then the oldest person can go with 7 of the remaining 12.

    The number of ways this can happen is \binom{12}{7}

    hence P=\frac{\binom{12}{7}}{\binom{14}{8}}
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