Answer:
50,803,200 ways
Step-by-step explanation:
In this situation, since you should alternate girl-boy or boy-girl, the line-up can either start with a boy or a girl kicking which would yield one of the two following patterns:
BGBGBGBGBGBGBG or GBGBGBGBGBGBGB.
For each of those patterns, there are 7! ways to arrange all boys and 7! ways to arrange all girls. The number of ways that a line-up can be made for one round of kicking is:
[tex]n=2*7!*7!\\n=2*(7*6*5*4*3*2)^2\\n=50,803,200\ ways[/tex]
There are 50,803,200 ways to set the line-up.
