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  • A group of 8 friends, including 3 siblings, is going to sit in a row for a photo. If the siblings must sit next to each other, in how many different ways can they be arranged?<div class='qna-op

A group of 8 friends, including 3 siblings, is going to sit in a row for a photo. If the siblings must sit next to each other, in how many different ways can they be arranged?

Option: 1

4,320

 


Option: 2

3,320

 


Option: 3

8,650

 


Option: 4

5,520


Answers (1)

best_answer

To calculate the number of different ways the group of 8 friends can be arranged in a row for a photo, with the 3 siblings sitting next to each other, we can treat the group of siblings as a single entity.

Now, we have 6 entities to arrange: the group of siblings and the remaining 5 friends.

The number of ways to arrange these 6 entities in a row is 6 !.

However, within the group of siblings, the siblings themselves can be arranged among themselves. Since there are 3 siblings, the number of ways to arrange them is 3 !.

Therefore, the total number of different ways to arrange the group of 8 friends, with the siblings sitting next to each other, is:

\mathrm{ 6 ! \times 3 !=720 \times 6=4,320 . }

Therefore, there are 4,320 different ways the group of 8 friends can be arranged in a row for a photo, with the siblings sitting next to each other.

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Kshitij

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