A soccer team consists of five girls and four boys. (All the players are distinguishable.) How many ways can they stand in line for a photograph, 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.