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  • A group of 5 friends wants to form a team of 3 for a sports event. However, two specific friends, Mark and Sarah, refuse to be on the team together. In how many ways can

A group of 5 friends wants to form a team of 3 for a sports event. 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

20


Option: 2

84


Option: 3

12


Option: 4

16


Answers (1)

best_answer

Number of friends = 5

Number of friends to be selected = 3

Number of ways to select 3 friends from 5 without Mark and Sarah together:

Selecting Mark:

We need to select 2 more friends from the remaining 4 (excluding Mark and Sarah). This can be done in \mathrm{C(4,2)} ways.

Selecting Sarah:

Similarly, we need to select 2 more friends from the remaining 4 (excluding Mark and Sarah). This can also be done in \mathrm{C(4,2)}ways.

\mathrm{\text { Total number of ways }=C(4,2)+C(4,2)=6+6=12 \text { ways. }}

Hence option 3 is correct.

 

Posted by

Kuldeep Maurya

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