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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 boys are standing next to each other?

 Jun 30, 2022
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Glue 2 of the boys together. There are \({4 \choose 2} = 6\) ways to do this. There are also 2 ways to order the 2 boys. 

 

Now, there are \(8!\) ways to order everyone (the 2 boys count as 1 person). 

 

This makes for \(8! \times 6 \times 2= \color{brown}\boxed{483840 }\) ways. 

 Jun 30, 2022

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