Question

In how many ways can 4 boys and 4 girls be arranged in a row such that no two boys and no two girls are next to each other?(A) 1032(B) 1152(C) 1254(D) 1432(E) 1564

Answer 1

Answer:

1152

Step-by-step explanation:

4 boys and 4 girls be arranged in a row such that no two boys and no two girls are next to each other.

Two boys and two girls are not next to each other. so one boy and one girl are next to each other in two ways.

BGBGBGBG, GBGBGBGB

4 boys are arranged in 4! ways and 4 girls are arranged in 4! ways

So number of ways = $2 \cdot 4! \cdot 4!=2 \cdot 24 \cdot 24=1152$