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  • A team of 4 engineers needs to be selected from a group of 7 candidates. However, two specific candidates, Alex and Emily, cannot be on the team together. In how many way

A team of 4 engineers needs to be selected from a group of 7 candidates. However, two specific candidates, Alex and Emily, cannot be on the team together. In how many ways can the team be formed?

Option: 1

90


Option: 2

60


Option: 3

20


Option: 4

40


Answers (1)

best_answer

Number of candidates = 7

Number of engineers to be selected = 4

Number of ways to select 4 engineers from 7 without Alex and Emily together:

Selecting Alex:

We need to select 3 more engineers from the remaining 6 (excluding Alex and Emily). This can be done in \mathrm{C(6,3)}ways.

Selecting Emily:

Similarly, we need to select 3 more engineers from the remaining 6 (excluding Alex and Emily). This can also be done in \mathrm{C(6,3)}ways.

\mathrm{\text{\text { Total number of ways }=C(6,3)+C(6,3)=20+20=40 \text { ways. }}}

Hence option 4 is correct.

 

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Sayak

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