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  • A group of 6 friends wants to form a team of 2 for a game. However, two specific friends, Mark and Sarah, refuse to be on the team together. In how many ways can the team

A group of 6 friends wants to form a team of 2 for a game. 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

5


Option: 2

6


Option: 3

9


Option: 4

10


Answers (1)

best_answer

Number of friends = 6

Number of friends to be selected = 2

Number of ways to select 2 friends from 6 without Mark and Sarah together:

Selecting Mark:

We need to select 1 more friend from the remaining 5 (excluding Mark and Sarah). This can be done in \mathrm{C(5,1)}ways.

Selecting Sarah:

Similarly, we need to select 1 more friend from the remaining 5 (excluding Mark and Sarah). This can also be done in \mathrm{C(5,1)}ways.

\mathrm{\text { Total number of ways }=C(5,1)+C(5,1)=5+5=10 \text { ways. }}

Hence option 4 is correct.

Posted by

Gautam harsolia

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