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 rCo 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 rCLlotteryrCY commission). Some people might speculate that the commission rCLfixesrCY the draw on different considerations. Sometimes they might record a higher success rate than choosing absolutely randomly. But thatrCOs another story, not related to maths...

The 2022/21 edition is discussed in this thread:
rCo https://groups.google.com/g/rec.sport.soccer/c/pnA8pSVJKrs
rCo UCL 2022/23 R16 2nd Legs [R]
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