Unformatted text preview: Consider the following problem: 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? Now we will look at the boy-girl line-up. For the boy-girl line-up, we have 6 boys that can take the ﬁrst kicking position, then we have 6 girls to choose from for the
second kicking position. For the next boy we will have 6 — 1 = 5 boys to choose from and then 6 — 1 = 5 girls to choose from.
This will continue until we are left with 1 boy for the next to last position and 1 girl for the very last position. B G B G B G B G B G B G
6 6 5 5 4 4 3 3 2 2 l 1 Therefore for the boy-girl line-up we will have 6! - 6! = 518400 ways to make the line-up. For either of the line-ups we will have 6! - 6!, so we will have a total number of line-up of ( 6! - 6! ) - 2:518400 - 2: 1036800. ...
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- Spring '10