A debate team consists of five girls and four boys. (Everyone is distinguishable.) How many ways can they stand in line, so that at least two of the girls are standing next to each other?
First, we choose the two girls to stand next to each other. We can do this in 5*4/2 = 10 ways. There are then 8 ways to choose the two places where they stand next to each other. There are 7 other people on the soccer team, so there are 10*8*7! ways to arrange the team members. Answer = 403200.
