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- A team of 5 players needs to be selected from a group of 9 athletes. However, two specific athletes, Jack and Olivia, cannot be on the team together. In how many ways can the team be formed?<di
A team of 5 players needs to be selected from a group of 9 athletes. However, two specific athletes, Jack and Olivia, cannot be on the team together. In how many ways can the team be formed?
52
84
70
12
Answers (1)
To calculate the number of ways the team can be formed, we need to consider two scenarios: Jack is on the team and Olivia is not, and Olivia is on the team and Jack is not.
Scenario 1: Jack is on the team and Olivia is not:
In this case, we need to select 4 more players from the remaining 7 athletes (excluding Jack and Olivia). The number of ways to do this is given by the combination formula:
Scenario 2: Olivia is on the team and Jack is not:
Similar to Scenario 1, we need to select 4 more players from the remaining 7 athletes (excluding Jack and Olivia). Again, the number of ways to do this is given by the combination formula:
Since these two scenarios are mutually exclusive (Jack and Olivia cannot be on the team together), we can simply add the results:
Therefore, there are 70 ways to form a team of 5 players, given that Jack and Olivia cannot be on the team together.
Hence option 3 is correct.
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