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  • A group of 8 friends wants to form a team of 4 for a trivia competition. However, two specific friends, Mark and Sarah, refuse to be on the team together. In how many way

A group of 8 friends wants to form a team of 4 for a trivia competition. However, two specific friends, Mark and Sarah, refuse to be on the team together. In how many ways can the team be formed?

Option: 1

63


Option: 2

84


Option: 3

96


Option: 4

40


Answers (1)

best_answer

To calculate the number of ways the team can be formed, we need to consider two scenarios: Mark is on the team and Sarah is not, and Sarah is on the team and Mark is not.

Scenario 1: Mark is on the team and Sarah is not:

In this case, we need to select 3 more friends from the remaining 6 (excluding Mark and Sarah). The number of ways to do this is given by the combination formula: \mathrm{C(6,3)=6 ! /(3 ! \times(6-3) !)=20 .}

Scenario 2: Sarah is on the team and Mark is not:

Similar to Scenario 1, we need to select 3 more friends from the remaining 6 (excluding Mark and Sarah). Again, the number of ways to do this is given by the combination formula: \mathrm{C(6,3)=6 ! /(3 ! \times(6-3) !)=20 .}

Since these two scenarios are mutually exclusive (Mark and Sarah cannot be on the team together), we can simply add the results:

\mathrm{\text{Number of ways = Scenario 1 + Scenario 2 = 20 + 20 = 40.}}

Therefore, there are 40 ways to form a team of 4 friends for the trivia competition, given that Mark and Sarah refuse to be on the team together.

Hence option 4 is correct.

 

Posted by

SANGALDEEP SINGH

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