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sport / rec.sport.soccer / Re: UCL Quarter Final draw

Re: UCL Quarter Final draw

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Subject: Re: UCL Quarter Final draw
From: ionsa...@gmail.com (Ion Saliu)
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by: Ion Saliu - Fri, 18 Mar 2022 11:00 UTC

On Friday, March 26, 2021 at 1:58:39 PM UTC+2, Ion Saliu wrote:
> To generalize total possibilities when matching elements 2 at a time; e.g.., a round of a competition as UEFA Champions League.
>
> The quarterfinal round consists of 8 teams and 4 matches.
>
> 1) Total possibilities where the team order counts:
> Arrangements (8, 4) = 8 * 7 * 6 * 5 = 1680 or
> Combinations (8, 4) * Permutations (4) = 70 * 24 = 1680.
> 2) Total possibilities where the team order does not count (as if all 8 teams play on a neutral site):
> Combinations (8, 4) * Arrangements (4, 2) = 70 * 12 = 840.
> For the round of 16, total possibilities are represented by a huge number — over 500 million!
>
> The computer can generate quite fast random sets. See just how difficult it is to get the right round setup (all matchups as drawn by the “lottery” commission). Some people might speculate that the commission “fixes” the draw on different considerations. Sometimes they might record a higher success rate than choosing absolutely randomly. But that’s another story, not related to maths...

The 2022/21 edition is discussed in this thread:

• https://groups.google.com/g/rec.sport.soccer/c/pnA8pSVJKrs
• UCL 2022/23 R16 2nd Legs [R]

Subject	Author
Re: UCL Quarter Final draw	Ion Saliu