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  • A group of 6 friends is going to sit in a row for a photo. However, two particular friends insist on sitting together. In how many different ways can they be arranged if they sit together, but not

A group of 6 friends is going to sit in a row for a photo. However, two particular friends insist on sitting together. In how many different ways can they be arranged if they sit together, but not necessarily next to each other?

Option: 1

120


Option: 2

240


Option: 3

420


Option: 4

320


Answers (1)

best_answer

To calculate the number of different ways the group of 6 friends can be arranged in a row for a photo, with two particular friends sitting together but not necessarily next to each other, we can treat the pair of friends as a single entity.

Now, we have 5 entities to arrange: the pair of friends and the remaining 4 individuals.
The number of ways to arrange these 5 entities in a row is 5 !.

However, within the pair of friends, the friends themselves can be arranged among themselves. Since there are 2 friends, the number of ways to arrange them is 2 !.

Therefore, the total number of different ways to arrange the group of 6 friends, with the two particular friends sitting together but not necessarily next to each other, is:

5 ! \times 2 !=120 \times 2=240 .

Therefore, there are 240 different ways the group of 6 friends can be arranged in a row for a photo, with the two particular friends sitting together but not necessarily next to each other.

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Rishi

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