Actually 40,320 different combinations of the draw.

Discussion in 'Bulletin Board ARCHIVE' started by Guest, Feb 18, 2008.

  1. Zuk

    Zukkster New Member

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    I think you've all got it wrong

    (n* (n-1))/2</p>

    (16 * 15)/2 = 120 different ties that could be played</p>

    That's means there are 120 different home or away combination of fixtures that Barnsley and the other teams could be playing.</p>

    I believe that paul d and jay have come up with the number of different cominations of orders that the balls come out of the bag. For example Barnsley vs Chelase is counted seperately depending upon whether it is the 1st, 2nd, 3rd, etc draw that comes out of the bag</p>

    With my calcualtion (if I've got it right) I'm saying Barnsely vs Chelsea is one possible fixture, and Chelsea vs Barnsley is another ... but the order of selection is not relevant and so I haven't accounted for it.</p>

    Dunno I think it's Coxter Groups and not Combinatorics you want to be looking at</p>

    </p>

    </p>
     
  2. pau

    paul.d Well-Known Member

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    not Impossible

    it's the fact that Barnsley eg can have 14 possible games . Each of those 14 games can then combine with the 14 games (minus the overlaps) that each of the other 7 teams can have
     
  3. pau

    paul.d Well-Known Member

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    haven't

    we have taken into account that eg AvB CvD EvF GvH is the same as eg AvB CvD GvH EvF when they are drawn in order
     
  4. Jay

    Jay Well-Known Member

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    Nope, it doesn't matter when they come out of the bag

    Using your formula if there were only 4 teams the answer would be 6. Using my formula, the correct formula, the answer would be 12 and I can easily prove that.

    Barnsley, Man Utd, Chelsea and Bristol Rovers are in the draw. So the possibilities are

    1Barnsley v Man Utd
    Chelsea v Bristol Rovers

    2Barnsley v Man Utd
    Bristol Rovers v Chelsea

    3Man Utd v Barnsley
    Chelsea v Bristol Rovers

    4Man Utd v Barnsley
    Bristol Rovers v Chelsea

    5Barnsley v Chelsea
    Man Utd v Bristol Rovers

    6Barnsley v Chelsea
    Bristol Rovers v Man Utd

    7Chelsea v Barnsley
    Man Utd v Bristol Rovers

    8Chelsea v Barnsley
    Bristol Rovers v Man Utd

    9Barnsley v Bristol Rovers
    Man Utd v Chelsea

    10Barnsley v Bristol Rovers
    Chelsea v Man Utd

    11Bristol Rovers v Barnsley
    Chelsea v Man Utd

    12Bristol Rovers v Barnsley
    Man Utd v Chelsea

    See, 12 combinations. Easy innit.
     
  5. Zuk

    Zukkster New Member

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    I kniw I've screwed up on something

    16 teams for a start.</p>

    I wasn't sure baout the division by two not accounting for home and away pairs.</p>

    I need to go away and think about it, but the figure you gave seems too high.</p>

    </p>

    What was the forumla you used to calculate 12?</p>
     
  6. Zuk

    Zukkster New Member

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    OK now I get it

    My calculation gives the number of pairs so in a league of 8 teams you've got (8 x 7)/2 = 28 pairs</p>

    That means 56 fixtures (home and away) in a league of 8 teams ... so there are 56 possible FIXTURES</p>

    However, you are right the number of permutations for the draw as in the different number of ways the draw could come out, and not the number of fixtures that could come out are the way you calculated</p>

    I was wrong, I'd misunderstood things. I always hated combination and permutation problems, I hate them even more now!!</p>
     

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