Question

You are getting a line-up ready for a school kickball game. you have 55 girls and 55 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

To solve this problem, we must first imagine out that the sequence of the children is either 
GBGBGB.... or BGBGBG....

So there are 2 possible sequence all in all. Now to solve for the total arrangements per sequence, the girls can be arranged in n! ways in their alloted spots, and so can the boys n! in their alternate spots, therefore:
Total arrangements = 2 * n! * n!

 

If n = 55

Total arrangements = 2 * 55! * 55!

Total arrangements = (The answer is very big ~almost infinite)

 

If n = 5

Total arrangements = 2 * 5! * 5!

Total arrangements = 28,800

 

So I believe the correct given is 5 boys and 5 girls and there are a total of 28,800 arrangements.