SOLUTION: A class of 10 students (5 boys and 5 girls) is lined up against a wall to have their class picture taken. How many different line-ups are possible if no two boys are standing next
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Question 912763: A class of 10 students (5 boys and 5 girls) is lined up against a wall to have their class picture taken. How many different line-ups are possible if no two boys are standing next to each other? Answer by Edwin McCravy(20055) (Show Source):
1. Chose the way to line up by gender, either BGBGBGBGBG or GBGBGBGBGB.
That's 2 ways.
2. For each of these ways we can arrange the boys 5! ways.
3. For each of these ways we can arrange the girls 5! ways.
Solution = 2*5!*5! = 2*120*120 = 28800
Edwin
