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Math Help - Probabilité

  1. #1
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    Probabilité

    Hi,

    a bag contains n balls, among them there has one, and another appointee named b. It takes balls p bag. What is the number of draws that contain a and b.

    A bag contains n balls, among them there has one appointed a and another appointed b. We take p balls from the bag. What is the number of draw that contains a and b? and the number of draw that contains just a and not b???
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  2. #2
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    Quote Originally Posted by lehder View Post
    Hi,

    a bag contains n balls, among them there has one, and another appointee named b. It takes balls p bag. What is the number of draws that contain a and b.

    A bag contains n balls, among them there has one appointed a and another appointed b. We take p balls from the bag. What is the number of draw that contains a and b? and the number of draw that contains just a and not b???
    Hi lehder,

    if "a" and "b" are in the selection of p balls, chosen from n,
    then there remain p-2 balls to choose from the remaining n-2.

    Hence there are \binom{n-2}{p-2} selections containing "a", "b" and p-2 other balls.


    If the p balls contain "a" but not "b",

    then we have n-2 balls to choose from and we require p-1 new additional balls to join with "a".

    Hence there are \binom{n-2}{p-1} selections of "a" with p-1 others, none of which are "b".
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