Question 1034403: If five girls and five boys stand in a circle, how many arrangements are possible provided they stand alternately (girl, boy, girl, boy, etc)?
Answer by robertb(5830)   (Show Source):
You can put this solution on YOUR website! Since the number of girls is equal to the number of boys, it wouldn't matter which group you first arrange in a circle.
Starting with the girls, they can be arranged in a circle in 4! = 24 ways.
There are now 5 spaces in between the girls where the boys can stand. Since the circularity is already broken, arranging the boys can be done in 5! = 120 ways.
Therefore, there are 24*120 = 2880 ways where the girls and boys stand alternately in a circle.
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