# Assigning swimming tracks!?

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• March 23rd 2012, 03:19 AM
timmeh
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
• March 23rd 2012, 06:03 AM
Plato
Re: Assigning swimming tracks!?
Quote:

Originally Posted by timmeh
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?
• March 23rd 2012, 06:16 AM
Ridley
Re: Assigning swimming tracks!?
1) $\frac{\binom 2 1 \binom 5 1}{\binom 7 2}$

2) $1 - \frac{\binom 3 2}{\binom 7 2}$
• March 25th 2012, 04:38 AM
timmeh
Re: Assigning swimming tracks!?
Ridley that seems to be correct. Could give me a more elaborate explanation? Especially 2)..?