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  • A company has 10 employees eligible for a promotion. However, two specific employees, Mike and Lisa, cannot be promoted together. The company wants to select a team of 3

A company has 10 employees eligible for a promotion. However, two specific employees, Mike and Lisa, cannot be promoted together. The company wants to select a team of 3 employees for the promotion. In how many ways can the team be formed?

Option: 1

52


Option: 2

46


Option: 3

53


Option: 4

56


Answers (1)

best_answer

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

Scenario 1: Mike is on the team and Lisa is not:

In this case, we need to select 2 more employees from the remaining 8 employees (excluding Lisa). The number of ways to do this is given by the combination formula:

\mathrm{C(8,2)=8 ! /(2 ! \times(8-2) !)=28 \text {. }}

Scenario 2: Lisa is on the team and Mike is not:

Similar to Scenario 1, we need to select 2 more employees from the remaining 8 employees (excluding Mike). Again, the number of ways to do this is given by the combination formula:

\mathrm{C(8,2)=8 ! /(2 ! \times(8-2) !)=28 \text {. }}

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

\mathrm{\text {Number of ways = Scenario 1 + Scenario 2 = 28 + 28 = 56. }}

Therefore, there are 56 ways to form a team of 3 employees for the promotion, given that Mike and Lisa cannot be promoted together.

Hence option 4 is correct.

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