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Math Help - C2 Ways in Urn Problem ?

  1. #1
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    C2 Ways in Urn Problem ?

    Hey Guys, i juz need some explanation about this problem which i attached as an image file ... as you can see the problem is already solved, i'm only concerned with the explanantion ...

    1) what is meant by 12C2 & 8C2 ways ?
    2)can u plz explain the terms that i highlighted with red ink like 8x7x6/2x1x6 and also 28/66 and etc.,

    Thanks
    Attached Thumbnails Attached Thumbnails C2 Ways in Urn Problem ?-01.jpg  
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  2. #2
    Super Member Anonymous1's Avatar
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    nC_k or {n\choose k} = \frac{n!}{(n-k)!k!}

    This means combination. If we have a total of n elements and we want to select a group of k of them. Then there are nC_k or "n choose k" ways to combine them.

    What exactly do you want explained about the highlighted problems?
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  3. #3
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    thanks for taking time and explaining the formula, "can u plz explain all the steps of this problem" ...

    1)how did this step happened ..." 8! / (2!x6!) = 8x7x6! / 2x1x6! ".
    2)how did i got 66 in the denominator of "28/66"
    3)why there's an exclamation point (!) ...???

    Thank You
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  4. #4
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    3)The exclamation point represents a factorial. For example:
    5!=5*4*3*2*1=120

    Anonymous1 already explained the combination part.

    1)All they did was expand 8! and the 2!
    8!=8*7-6*5*4*3*2*1 and 2!=2*1

    2)66 is the number of ways that two balls can be chosen from the urn. It's found by:

    <br /> <br />
{12\choose 2} = \frac{12!}{(12-2)!2!}= \frac{12!}{10!*2!}=66<br />

    This is explained in the solution to the problem that you posted
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  5. #5
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    Thank you very much downthesun01, Great Explanation ... i'm all cleared out with my doubts now ... and thanks to Anonymous1 too ...

    Cheers Guys
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