After play-in games, the NCAA basketball tournament involves 64 teams, arranged in a bracket that specifies who plays whom in each round. (The winner of each game goes on to the next round; the loser...

After play-in games, the NCAA basketball tournament involves 64 teams, arranged in a bracket that specifies who plays whom in each round. (The winner of each game goes on to the next round; the loser is eliminated. See Figure 9.25.) How many different outcomes (that is, lists of winners of all games) of the tournament are there?