In how many ways can 4 boys and 4 girls be seated in a row if each boy must sit next to a girl?
576
640
192
864
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 ways.
Now, we have 4 entities to arrange in a row. Since these entities are distinct, they can be arranged in =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:
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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