UK Football League Coincidence

John B

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Joined
Mar 17, 2013
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3
In the English Championship division, there are 24 teams, 8 of which have names starting with the letter B (-e.g.Bolton). Tonight,(5th March 2013) all 24 teams in this division are playing each other. The 8 teams starting with B are playing each other, by a coincidence., i.e. 4 of the games involve these 8 teams ( there are 2 teams per game) What is the probability of this happening ? I'd really like to know how to work this out.
 
In the English Championship division, there are 24 teams, 8 of which have names starting with the letter B (-e.g.Bolton). Tonight,(5th March 2013) all 24 teams in this division are playing each other. The 8 teams starting with B are playing each other, by a coincidence., i.e. 4 of the games involve these 8 teams ( there are 2 teams per game) What is the probability of this happening ? I'd really like to know how to work this out.


There are \(\displaystyle \dfrac{24!}{2^{12}(12!)}\) ways the pair these twenty-four teams.

There are \(\displaystyle \dfrac{8!}{2^{4}(4!)}\cdot\dfrac{16!}{2^{8}(8!)}\) ways the pair the eight B teams and the others.
 
There are \(\displaystyle \dfrac{24!}{2^{12}(12!)}\) ways the pair these twenty-four teams.

There are \(\displaystyle \dfrac{8!}{2^{4}(4!)}\cdot\dfrac{16!}{2^{8}(8!)}\) ways the pair the eight B teams and the others.

Thank you pka but I really would like a clearer explanation of how you arrive at your statements and would like you to end up with a probability.
 
Thank you pka but I really would like a clearer explanation of how you arrive at your statements and would like you to end up with a probability.


Do you understand un-order partition? If you do, then those two calculate the number of ways to pair 2n objects into n pairs. Divide the total into the subcase to get the probability.

If you are not up on counting theory, then I am not prepared to give you a tutorial on un-order partition.
 
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