statistics

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A jar contains 7 red balls, 5 green balls, 4 blue balls, and 3 white balls. A sample of size 7 balls is selected at random without replacement . Find t the probability that sample contains two red balls, 2 green balls, 2 blue balls, and 1 white ball.

  • probability -

    Let's simplify the problem to having
    7 red balls,
    5 green balls, and
    4 blue balls
    (for a total of 16).
    Find the probability of drawing
    2 red balls, 2R
    2 green balls, 2G
    2 blue balls, 2B
    (total of 6 balls), then

    Below we will use the notation of
    (n,r)=combination (n,r)
    =n!/((n-r)!r!)

    Number of ways of drawing
    2R,2G and 2B would be
    for 2R: (7,2)=21
    for 2g: (5,2)=10
    for 2B: (4,2)=6
    and number of ways of drawing 6 balls out of 16: (16,6)=8008
    So probability
    P(2R+2G+2B)=(7,2)(5,2)(4,2)/(16,6)
    =21*10*6/8008
    =45/286

    Extend the idea to the problem in hand, and post for answer checking if you wish.

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