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  • A group of 8 friends, including 4 couples, is going to sit in a row for a photo. If each couple must sit together, in how many different ways can they be arranged?

A group of 8 friends, including 4 couples, is going to sit in a row for a photo. If each couple must sit together, in how many different ways can they be arranged?

 

Option: 1

325


Option: 2

185


Option: 3

384


Option: 4

422


Answers (1)

best_answer

To calculate the number of different ways the group of 8 friends can be arranged in a row, with each couple sitting together, we can consider each couple as a single entity.

Since there are 4 couples, we have 4 entities to arrange. The number of different ways to arrange these entities is given by 4 !.

However, within each couple, the individuals can be arranged among themselves. Since there are 2 individuals in each couple, the number of ways to arrange each couple is 2 !.

Therefore, the total number of different ways to arrange the group of 8 friends, with each couple sitting together, is:

4 ! \times(2 !)^4=24 \times 16=384

Therefore, there are 384 different ways the group of 8 friends can be arranged in a row, with each couple sitting together.

Posted by

Shailly goel

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