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More combinations

  1. Sep 4, 2011 #1
    1. The problem statement, all variables and given/known data

    From a group of 3 freshman, 4 sophomores, 4 juniors, and 3 seniors, a committee of size 4 is randomly selected. Find the probability that the committee will consist of:

    a) 1 from each class
    b) 2 sophomores and 2 juniors
    c) only sophomores and juniors

    2. Relevant equations

    How do you write "x choose n" in latex? For now I'll write (xCn)


    3. The attempt at a solution

    I figured there (14C4) different committees, giving 1001 committees.

    a) [(3C1)(4C1)(4C1)(3C1)]/1001 = 144/1001

    b) [(4C2)(4C2)]/1001 = 36/1001

    c) 2/1001


    Is this correct?
     
  2. jcsd
  3. Sep 4, 2011 #2

    gb7nash

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    How did you get c)? (it's wrong)
     
  4. Sep 4, 2011 #3

    tiny-tim

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    Hi ArcanaNoir! :smile:

    (try using the X2 and X2 icons just above the Reply box … alternative nCm in latex is ^nC_m :wink:)

    Your (a) and (b) look ok. :smile:

    Your (c) is the answer for "only sophomores or only juniors". :redface:

    (frankly, I don't know what (c) means … eg is 1 sophomore and 3 juniors sophomores ?)
     
  5. Sep 4, 2011 #4

    gb7nash

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    I agree. c) is poorly worded. I think the only condition is that no. sophomore >= 1 and no. junior >= 1, otherwise it's the same question as b), or 2 like the OP said.
     
  6. Sep 4, 2011 #5

    I like Serena

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    Funny, I interpreted it as:
    only from the group of all juniors and all sophomores.

    So: no. sophomores ≥ 0 and no. juniors ≥ 0.
     
    Last edited: Sep 4, 2011
  7. Sep 4, 2011 #6

    tiny-tim

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    Hi I like Serena! :smile:

    I think that's what it's meant to mean, but I don't think it's what it actually means! :biggrin:
     
  8. Sep 4, 2011 #7

    I like Serena

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    Hi TM! :smile:

    Errr.... so 0 juniors and 4 sophomores, would qualify,
    but 1 junior and 3 sophomores would not? :confused:
     
  9. Sep 4, 2011 #8

    tiny-tim

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    uhh? :confused:

    0 isn't plural :wink:
     
  10. Sep 4, 2011 #9

    tiny-tim

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    zero apples isn't apples!

    if you have zero apples, you don't have apples :redface:
     
  11. Sep 4, 2011 #10

    I like Serena

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    Okay.

    So are you suggesting that c) could be interpreted as:
    no. sophomores ≥ 2 and no. juniors ≥ 2?​


    Or more strongly, that this is what it actually means?
     
    Last edited: Sep 4, 2011
  12. Sep 4, 2011 #11

    tiny-tim

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    Yup! :biggrin:
     
  13. Sep 4, 2011 #12
    Gee guys, if you had just waited.. C was supposed to be only sophomores OR only juniors. My prof's english is bad.
     
  14. Sep 5, 2011 #13

    I like Serena

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    Wait?!
    And miss out on all the fun and conjecture?
    Nah! :smile:

    Anyway, I was kind of impressed to find out that "only sophomores and juniors" translates into "exactly 2 sophomores and 2 juniors".
    Who'd have thunk! :wink:
     
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