This morning's CL draw fell along lines that are likely to generate some suspicious of it being rigged - i.e. the strongest teams all avoided each other. I was trying to figure out the approximate probability of this draw. I imagine it's a relatively simple question and I want to check my thoughts. Basically I would divide the 8 teams into 2 pots: Pot 1-Stronger and Pot 2-Weaker (Dortmund and Juventus are probably the only debatable choices in my lists)
Pot 1: Barcelona Real Madrid Bayern Munich Dortmund
Pot 2: Juventus PSG Gala Malaga
My question is: what is the probability of all 4 matches containing exactly one Pot 1 team and one Pot 2 team? For any given draw the probability is 4/7 that you get a team from the opposite pool but what happens then? How do I sum the probabilities for the remaining draws (presumably the drawn teams are taken out of the pool for the next round)?