Currently three Spanish teams are in the quarter-finals of the Championsleague. What are the odds that none of those teams play each other during the quarter finals?
All possible combinations is $8!$, is that correct?
But how many combinations are there in which Spanish teams do not play each other?
I tried something like this: Let's say the first team is Spanish, then it only has five options for non-Spanish teams etc... but it turns out it matters in what order you would pick the Spanish or non-Spanish teams, so now I am stuck. Any help would be appreciated.