Final answer:
In each game, there are two possible outcomes: the American League team wins (A) or the National League team wins (N). The total number of different orders is found by multiplying the number of possibilities for each game. This is because, for each game, you have two choices (A or N), and the total number of different orders is calculated by raising 2 to the power of the number of games in the series.
Step-by-step explanation:
a) For a four-game series:
There are two possibilities for the winning team in each game: American League (A) or National League (N). Therefore, the total number of different orders is 2⁴= 16.
b) For a five-game series:
Similar to the four-game series, there are two possibilities for the winning team in each game. Therefore, the total number of different orders is 2⁵ = 32.
c) For a six-game series:
Again, two possibilities for the winning team in each game result in 2⁶ = 64 different orders.
d) For a seven-game series:
With two possibilities for each of the seven games, the total number of different orders is 2⁷ = 128.