LUANDATO wrote:Six students - 3 boys and 3 girls - are to sit side by side for a makeup exam. How many ways could they arrange themselves given that no two boys and no two girls can sit next to one another?
A) 12
B) 36
C) 72
D) 240
E) 720
The boys and girls must ALTERNATE.
Case 1:
BGBGBG
Within the 3 red positions, the number of ways to arrange the 3 boys = 3! = 6.
Within the 3 blue positions, the number of ways to arrange the 3 girls = 3! = 6.
To combine the 6 options for the boys with the 6 options for the girls, we multiply:
6*6 = 36.
Case 2:
GBGBGB
Case 2 will yield the same number of ways as Case 1:
36.
Total ways = Case 1 + Case 2 = 36+36 = 72.
The correct answer is
C.
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