Sample Space for Conventional Knock-Out Tournament

[Alexsandro]

Somebody could help me with this question?

A conventional knock-out tournament begins with 2^n competitors and has n rounds. There are no play-offs for the positions 2, 3, ..., 2^(n)-1, and the initial table of draws is specified. Give a concise description of the sample space of all possible outcomes.

thanks,

Alexsandro

 

[HallsofIvy]

That depends upon what you consider an outcome! If you are only asking "who won the tournament", then the set of possible outcomes is precisely the set of players- because anyone of them could win the tournament. If you are thinking of the "rankings" awarded by this tournament: the winner, the person who only lost in the final round (and so comes in second), the two people who lost to those first two (and so share third and fourth places), etc. that's a much more complicated question!