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  1. #1
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    combination

    $\displaystyle 8 $ bottles of zinfandel

    $\displaystyle 10 $ bottles of merlot

    $\displaystyle 12 $ bottles of cabaret.

    (a) If he wants to serve $\displaystyle 3 $ bottles of zinfandel and serving order is important, how many ways are there to do this?

    $\displaystyle \frac{8!}{5!} = 336 $


    (b) If $\displaystyle 6 $ bottles of wine are to be randomly selected from the $\displaystyle 30 $, how many ways are there to do this?

    $\displaystyle \binom{30}{6} = 593,775 $

    (c) If $\displaystyle 6 $ bottles are randomly chosen, how many ways are there two bottles of each variety being chosen?


    (d) If $\displaystyle 6 $ bottles are randomly chosen, what is the probability that this results in two bottles of each variety being chosen.

    (e) If $\displaystyle 6 $ bottles are randomly chosen, what is the probability that they are all the same variety?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by shilz222 View Post

    (c) If $\displaystyle 6 $ bottles are randomly chosen, how many ways are there two bottles of each variety being chosen?
    $\displaystyle { 8 \choose 2} {10 \choose 2} {12 \choose 2}$

    (d) If $\displaystyle 6 $ bottles are randomly chosen, what is the probability that this results in two bottles of each variety being chosen.
    $\displaystyle \frac {{ 8 \choose 2} {10 \choose 2} {12 \choose 2}}{{ 30 \choose 6}}$

    (e) If $\displaystyle 6 $ bottles are randomly chosen, what is the probability that they are all the same variety?
    $\displaystyle \frac {{ 8 \choose 6} + {10 \choose 6} + {12 \choose 6}}{{30 \choose 6}}$

    why is that?
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  3. #3
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    There are $\displaystyle \binom{8}{6} $ ways to choose all zinfandel, etc..
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