Suppose we are at a tournament with 30 competitors, and 5 rounds. Each rounds consists of 15 matches (2 competitors each) in which each competitor has a 50% chance of winning. After the 5 rounds there are quarter finals, in which the top 8 go on to compete each other.
The question is, what is the probability that the top 8 won all their matches in the first 5 rounds. That means that they can't have met each other. In addition, pairing always have to be different for every round.
This one has me stumped. I'm almost losing sleep over it. Any ideas?