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  • In how many ways can 4 boys and 4 girls be seated in a row if each boy must sit next to a girl?    Option: 1 576</

In how many ways can 4 boys and 4 girls be seated in a row if each boy must sit next to a girl?

 

 

Option: 1

576


Option: 2

640


Option: 3

192


Option: 4

864


Answers (1)

best_answer

To find the number of ways to seat 4 boys and 4 girls in a row such that each boy must sit next to a girl, we can approach the problem by treating each boy-girl pair as a single entity.

We have 4 boy-girl pairs, so there are 4 entities to arrange. Within each entity, the boy and girl can be arranged in 2 ! =2  ways.
Now, we have 4 entities to arrange in a row. Since these entities are distinct, they can be arranged in 4 !  =24 ways 
Therefore, the total number of valid seating arrangements is given by multiplying the number of arrangements within each entity and the number of arrangements of the entities themselves:  
2 ! \times 2 ! \times 2 ! \times 2 ! \times 4 !=192 
Hence, there are 192 different ways to seat 4 boys and 4 girls in a row, satisfying the condition that each boy must sit next to a girl.

 

 

 

 

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