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anonymous

  • 4 years ago

Assume that the committee consists of 8 Republicans and 5 Democrats. A subcommittee of 4 is randomly selected from all subcommittees of 4 which contain at least 1 Democrat. What is the probability that the new subcommittee will contain at least 2 Democrats?

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  1. anonymous
    • 4 years ago
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    good lord

  2. anonymous
    • 4 years ago
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    lets see if we can figure out how many subcommittees contain at least one democrat, and i guess the best way to do it is figure out how many contain no democrats and subtract it from the total possible subcommittees

  3. anonymous
    • 4 years ago
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    these things ar ekilling me and i have to have these done by 730 am

  4. anonymous
    • 4 years ago
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    number of subcommittees with not restriction is \[\dbinom{13}{4}=\frac{13\times 12\times 11\times 10}{4\times 3\times 2}=715\]

  5. anonymous
    • 4 years ago
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    number of subcommittees that are all republicans are \[\frac{8\times 7\times 6\times 5}{4!}=70\] so i guess we have \[715-70=645\] total subcommittees that contain at least one democrat

  6. anonymous
    • 4 years ago
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    that will be our denominator. now we have to figure out, of these 645 subcommittees with at least one democrat, how many have at least two

  7. anonymous
    • 4 years ago
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    ok exactly one democrat number of ways would be \[\dbinom{5}{1}\dbinom{8}{3}\] aka \[5\times 56=280\]

  8. anonymous
    • 4 years ago
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    so subtract this off from 645 to get the number that contain more than 1 democrat. you get \[645-280=365\] so our answer is \[\frac{365}{645}\]

  9. anonymous
    • 4 years ago
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    that didnt work

  10. anonymous
    • 4 years ago
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    you sure? i think the method is right. maybe a calculation error?

  11. anonymous
    • 4 years ago
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    the more i think about it the more i think it is right. do you have an answer?

  12. anonymous
    • 4 years ago
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    you are right

  13. anonymous
    • 4 years ago
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    whew!!

  14. anonymous
    • 4 years ago
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    im sorry not sure why it didnt work first time

  15. anonymous
    • 4 years ago
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    ok did you try the other one i sent? is this an on line class?

  16. anonymous
    • 4 years ago
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    no but home work is submitted online...

  17. anonymous
    • 4 years ago
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    oh i see. have fun!

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