There are 32 teams in a traditional knockout tournament. Each of these 32 teams are of a different quality and can be distinctly ranked from 1st to 32nd in terms of ability. Assume that a higher-ability team always beats a lower-ability team. The teams are randomly seeded in the schedule of this knockout tournament. What is the probability that the second-best team meets the third best team in the semi-finals?
2026-04-08 19:11:11.1775675471
Probability of two teams matching up in semi-finals of 32-team knockout tournament.
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To explain Lourran answer's . Imagine an array of 32 numbers from 1 to 32 randomly distributed, such that one of two neighbour numbers proceed to next round based on their ranking.
The rank 1 can be in 32/32 places. The rank 2 cannot be in the same half as 1 (else they will meet before or in the semi finals) so it has 16/31 choices. The rank 3 cannot be in same quarter as rank 2 and cant be in same half as 1, so 8/30 choices. SO the answer is 32/32 * 16/31 * 8/30