Question 331888: In how many arrangements can 7 women and 7 men be placed in a line if the women and men alternate? 50803
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! First is the choice of whether to start with a man or a woman. Then there is a choice from among the 7 of that gender, then a choice from among the 7 of the other gender, then a choice from the 6 remaining of the first gender, then a choice from among the 6 remaining of the second gender, etc.
So the number of arrangements would be:
2*7*7*6*6...*1*1
Rearranging these, using the oommutative property, we get:
2*7!*7!
Since 7! = 5040, this becomes:
2*5040*5040
I'll leave it to you to multiply this out.
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