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Math Help - Assigning swimming tracks!?

  1. #1
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    Assigning swimming tracks!?

    Problem: 7 swimmers are participating in a swimming match; 3 Americans, 2 Germans, 1 Australien and 1 Dutch. The swimming tracks 1 till 7 are randomly assigned.

    Two questions:
    1) What is the chance that 1 of the Germans is swimming in a outer track (so that would mean 1 german in track 1 or track 7)
    2) What is the chance that at least 1 of the non-Americans is swimming in a outer track?

    Could somebody please tell me how to calculate this?

    I think I should divide the number of succesful outcomes by the total number of outcomes.

    Total number = 7! = 5040

    But how do I find the number of succesful outcomes in this case...

    Answers should be
    1) 0.476
    2) 0.857
    Last edited by timmeh; March 23rd 2012 at 04:38 AM.
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  2. #2
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    Re: Assigning swimming tracks!?

    Quote Originally Posted by timmeh View Post
    Problem: 7 swimmers are participating in a swimming match; 3 Americans, 2 Germans, 1 Australien and 1 Dutch. The swimming tracks 1 till 7 are randomly assigned. Two questions:
    1) What is the chance that 1 of the Germans is swimming in a outer track (so that would mean 1 german in track 1 or track 7)
    2) What is the chance that at least 1 of the non-Americans is swimming in a outer track?
    Answers should be: 1) 0.476 2) 0.857
    Are you translating these questions into English?
    I ask because it took me several tries to get the given answer to question 1).
    That answer is to this question: “What is the probability that exactly one German is in an outside lane”?
    BUT the way the question is written it means at least one.

    BTW: \dfrac{4\cdot 5\cdot 5!}{7!}=0.47619 WHY?
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  3. #3
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    Re: Assigning swimming tracks!?

    1) \frac{\binom 2 1 \binom 5 1}{\binom 7 2}

    2) 1 - \frac{\binom 3 2}{\binom 7 2}
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  4. #4
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    Re: Assigning swimming tracks!?

    Ridley that seems to be correct. Could give me a more elaborate explanation? Especially 2)..?
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