You are getting a line-up ready for a school kickball game. you have 77 girls and 77 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?

1. Since each child kicks the same number of times, it is not important whether he or she kicks 1 time, 2, 3 or more times. So let all of them kick 1 time.

2. assume we start with a girl. We can start with either of the 77 girls, then second is a boy which can be either of the 76, the third is a girl which can be either of the 76 remaining, then the forth is one of the 76 boys...

3. So starting with a girl we have

77*(77)*76*(76)*75*(75)....*2*(2)*1*(1)=77!*77!

4. OR we could have started with a boy, where we would get again 77!*77!

5. 77!*77!+77!*77!=2