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  • In how many ways can 4 boys and 4 girls be seated in a row such that no two girls sit next to each other?  Option: 1 1920<br

In how many ways can 4 boys and 4 girls be seated in a row such that no two girls sit next to each other?

 

Option: 1

1920


Option: 2

2160


Option: 3

2880


Option: 4

3240


Answers (1)

best_answer

We can arrange the 4 boys in 4 ! = 24  ways. Then, we can insert the 4 girls into the 5 spaces between the boys, in any order, in 5 ! ways. However, for each of these arrangements, the two end spaces cannot be occupied by girls. Therefore, we must subtract the arrangements where a girl is in one of the two end spaces. There are 2 ways to select which end space is occupied, and 4 ! \times 4 ! ways to arrange the boys and girls in the remaining spaces. Therefore, the total number of ways is 4 ! \times 5 ! \times-2 \times 4 ! \times 4 !=1920

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Divya Prakash Singh

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