Question

You are getting a line-up ready for a school kickball game. You have 7 girls and 7 boys. The rules state each child must kick the same number of times and alternate girl-boy or boy-girl. How many ways can a line-up be made for one round of kicking?

Answer 1

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:

$n=2*7!*7!\\n=2*(7*6*5*4*3*2)^2\\n=50,803,200\ ways$

There are 50,803,200 ways to set the line-up.