Question 1021131: in how man different ways can 5 girls and 5 boys form a circle such that the boys and the girls alternate?
a.2880
b.1400
c.1200
d.3212
Answer by robertb(5830)   (Show Source):
You can put this solution on YOUR website! First arrange the girls in a circle. (In this case it doesn't really matter whether the girls are seated first or last, because the number of girls is the same as the number of boys.) The number of ways of doing this is 4! = 24, since this is a cyclic permutation.
After the girls are seated, there are 5 spaces in-between where the boys can be inserted. There are 5! = 120 ways of doing this.
Therefore there are 24*120= 2,880 ways of forming a circle where 5 boys and 5 girls sit alternatingly.
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