Lunchtime combinatorics

Ok, it's been a while since I did any of this, but this is how (I think) you calculate it.

Consider a league with 8 teams. There are (8 choose 2) * (6 choose 2) * (4 choose 2) = 28 * 15 * 6 = 2520 possible fixture combinations.
Of those, how many consist of fixtures played only between teams in the same half? In that case, there
are (4 choose 2) = 6 possible fixtures combinations in the top half and the same in the bottom half. So the total combinations = 36.
Therefore the probability in a league of 8 teams is 36/2520 = 0.014.

There are 20 teams in the EPL so there are (20 choose 2) * (18 choose 2) *...(4 choose 2) = 2.376*10^15 (2 and a bit million billion) possible fixture combinations.
Of those, there are ((10 choose 2) * (8 choose 2) * (6 choose 2) * (4 choose 2))^2 = 113,400^2 possible fixture combinations consisting of games only between teams
in the same half. So the probability is (approx) 0.000005.

Is this right?

Posted By: yarmyyarmy on November 16th 2011 at 13:40:00

Message Thread

Lunchtime combinatorics (General Chat) - yarmyyarmy, Nov 16, 13:40:00
- seems rather long odds (General Chat) - SCC 28, Nov 16, 13:43:39
  - Which is why I'm suspicious of my own logic a bit (General Chat) - yarmyyarmy, Nov 16, 13:47:32
    - might have a forumula actually (General Chat) - SCC 28, Nov 16, 13:56:22
      - hmmmm (General Chat) - SCC 28, Nov 16, 14:04:07
        
        ah but that's just the correct order isn't it (General Chat) - SCC 28, Nov 16, 14:07:53
        
        That's not the same though is it (n/m) (General Chat) - yarmyyarmy, Nov 16, 14:06:22
        
        agreed (General Chat) - SCC 28, Nov 16, 14:08:56
- Yes, that's right (General Chat) - duke of york, Nov 16, 13:43:17

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