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Math Help - Probability Question

  1. #1
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    Probability Question

    There are 5 four person flats
    there are 8 groups of four going for these 5 flats
    what is the probability that a particular 3 groups (groups A B and C) all get flats
    if its done by random draw.


    Thank you



    ViperRobK
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  2. #2
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    Hello, ViperRobK!

    There are 5 four-person flats.
    there are 8 groups of four going for these 5 flats.
    What is the probability that a particular 3 groups (groups A B and C) all get flats
    if its done by random draw?
    Who made up this problem?
    And why did they make it more confusing than necessary?

    There are eight people from which five will be randomly chosen.
    What is the probability that 3 particular people (A,B,C) are chosen?


    There are: . _8C_5\:=\:{8\choose5} \:=\:56 possible outcomes.


    There is 1 way for A, B, C to be chosen.
    We must choose 2 more people from the other 5 people: . {5\choose2} \:=\:10 ways.
    . . Hence, there are: . 1\cdot10\:=\:10 ways that A,B,C can be chosen.


    Therefore: . P(\text{A,B,C chosen}) \:=\:\frac{10}{56} \:=\:\frac{5}{28}

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