Question

You are getting a line-up ready for a school kickball game. You have 6 girls and 6 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:

The total number of line-up that can be made is 1,036,800.

Step-by-step explanation:

The number of girls in the game is, 6.

The number of boys in the game is, 6.

The line-up is set such that boys and girls are alternatively placed.

The possible arrangements are:

{B G B G B G B G B G B G} OR {G B G B G B G B G B G B}

There are 6 places that can be occupied by the boys and 6 places that can be occupied by the girls.

The 6 boys can be arranged in 6! ways.

The 6 girls can be arranged in 6! ways.

And there are 2 possible arrangements.

The total number of arrangements is:

$2\times 6!\times 6!=1036800$

Thus, the total number of line-up that can be made is 1,036,800.