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  • A team of 3 engineers needs to be selected from a group of 6 candidates. However, two specific candidates, Alex and Emily, cannot be on the team together. In how many way

A team of 3 engineers needs to be selected from a group of 6 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

11


Option: 2

20


Option: 3

13


Option: 4

30


Answers (1)

best_answer

Number of candidates = 6

Number of engineers to be selected = 3

Number of ways to select 3 engineers from 6 without Alex and Emily together:

Selecting Alex:

We need to select 2 more engineers from the remaining 5 (excluding Alex and Emily). This can be done in \mathrm{C(5,2)}ways.

Selecting Emily:

Similarly, we need to select 2 more engineers from the remaining 5 (excluding Alex and Emily). This can also be done in \mathrm{C(5,2)}ways.

\mathrm{\text{\text { Total number of ways }=C(5,2)+C(5,2)=10+10=20 \text { ways. }}}

Hence option 2 is correct.

 

Posted by

HARSH KANKARIA

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