Dear Uncle Colin,
I’m trying to figure out how many possible draws there are for the Champions’ League quarter-finals. There are eight teams involved, and let’s assume first leg home advantage doesn’t matter (so A vs B is the same as B vs A) and there’s no restriction on which teams can be matched. How would you work it out?
- Understanding Every Football Algorithm
Hi, UEFA, and thanks for your message!
Here’s how I would work it out. I would:
All in all, there are $7 \times 5 \times 3 \times 1 = 105$ possible draws.
In that case, each of the 105 distinct draws could be arranged in any one of 16 ways (each of the four matches could be reversed).
That gives a total of $105 \times 16 = 1680$ possible draws.
Hope that helps!
- Uncle Colin