To win the World Series, a baseball team must win 4 games out of a maximum of 7 games. To solve the problem, list the possible arrangements of losses and wins.
How many ways are there of winning the World Series in exactly 6 games if the winning team wins the first game?
a. 4 ways b. 6 ways c. 3 ways d. 5 ways
b. 6 ways
To determine the possible arrangements of losses and wins in a 7-game World Series, we can use a combination of wins and losses.
In a 7-game series, there are a total of 4 wins needed to secure the championship. Since the winning team wins the first game, they only need to win 3 more games.
To find the number of ways of winning the World Series in exactly 6 games if the winning team wins the first game, we need to consider the possible arrangements of wins and losses in the remaining 5 games.
Since the winning team has already won the first game, they need to win 3 more games out of the remaining 5. This can be represented as:
WWLWL, WLWWW, WWLWW, WWLWW, WWLWW, WWLWW
In these arrangements, 'W' represents a win and 'L' represents a loss.
Therefore, there are a total of 4 ways of winning the World Series in exactly 6 games if the winning team wins the first game.
The correct answer is:
a. 4 ways