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Thread: Small combinatorics question

  1. #1
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    Lightbulb Small combinatorics question

    Hey all! I was hoping you could help me get a 'second opinion' to a problem I ran into. It's most likely one of the most basic combinatorics question one can run into but I'm notoriously awful at it.
    Here goes:

    There are 8 tops in a closet. 3 red ones by the sizes of S,M and L; 3 blue ones, sizing S,M and L again, and 2 white ones, which are M and L.
    2 tops are chosen randomly.
    What's the probability that the chosen tops will not be white or/and small? *clarification: We need 2 shirts to be a combination of blue/red/medium/large.

    I tried to solve this using combinatorics as well as conditional probability, both led me to different answers.

    using combinatorics, I did-
    [(2 out of 3)+(2 out of 3)+(1 out of 3)*(1 out of 3)]/(2 out of 8)
    meaning we either select 2 shirts out of the 3 red OR 1 out of the red, 1 out of the blue, OR 2 out of the 3 blue ones.

    My husband thought we should do it this way:
    [(6 out of 8)*(4 out of 6)+(5 out of 7)*(3 out of 5)]\(2 out of 8)
    so- we choose total 6 out of the 8 tops, (3 blue, 3 red), time it by the selection of sizes we want, and we repeat this picking the second top.
    His end result was >1 however.

    I tried using conditional probability too, and basically did (3/8*1/3)*2

    Will gladly appreciate input about this as I'm a bit confused

  2. #2
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    Re: Small combinatorics question

    (4 choose 2) / (8 choose 2) = 3/14


    (4/8)*(3/7) = 3/14

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