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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?

 Mar 16, 2020
 #1
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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.

 Mar 16, 2020
 #2
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**** deleted ****

 Mar 16, 2020
edited by ElectricPavlov  Mar 16, 2020

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