Suppose four teams, numbered one through four, play asingle-elimination tournament, consisting of three games. Two teamsplay each game and one of them wins; ties do not occur. Thetournament bracket is as follows: teams one and another team playeach other in the first game and the remaining two teams play eachother in the second game; the winner of the first game plays thewinner of the second game in the third game.
Define a set ΩΩ so the elements of ΩΩ correspond to the possibleoutcomes of the tournament. An element of ΩΩspecifies the entiresequence of outcomes of the games. How many outcomes are there forthe combination of what bracket is used and the game outcomes?(Assume the order the two games are played in the first round doesnot matter. For example, they could be simultaneous.)
