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  • In how many ways can 6 people be seated in a row if 2 particular people refuse to sit next to each other?Option: 1 720<div class='qna-o

In how many ways can 6 people be seated in a row if 2 particular people refuse to sit next to each other?

Option: 1

720


Option: 2

960


Option: 3

1080


Option: 4

1440


Answers (1)

best_answer

There are 6 ! ways to arrange the 6 people in a row. However, since the people in each couple can be arranged in 2 !   ways, we must divide by 2 ! for each of the 3 couples, giving us a total of \frac{6 !}{2 ! \times 2 ! \times 2 !}=720

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