The 2023 Women’s World Cup will feature 32 teams. At the end of the tournament, the teams are ranked from 1 to 32. (1) Four teams will make the semi-finals, where the winners play in the final and the losers meet in the 3rd place game, after which the 1st through 4th place positions are At the start of the tournament, how many different possible final arrangements are there of teams in 1st through 4th place? (2) New Zealand and Australia are co-hosting the How many final rankings of the
The 2023 Women’s World Cup will feature 32 teams. At the end of the tournament, the teams are ranked from 1 to 32.
(1) Four teams will make the semi-finals, where the winners play in the final and the losers meet in the 3rd place game, after which the 1st through 4th place positions are At the start of the tournament, how many different possible final arrangements are there of teams in 1st through 4th place?
(2) New Zealand and Australia are co-hosting the How many final rankings of the 32 teams have either New Zealand or Australia in 1st place (as the champion)? Briefly describe how you arrived at your solution.
(3) How many final rankings of the 32 teams have neither New Zealand nor Australia in 1st place? Briefly describe how you arrived at your solution.
(4) The USA is the clear-cut best team in the world, followed by Germany and Suppose there is an upset and none of those 3 teams make the final (so none finish in first or second). How many different final rankings are there of the 32 teams? Describe how you arrived at your solution.
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