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A speech class has $4$ freshmen and $3$ sophomores. (Everyone is distinguishable.) In how many ways can they stand in line, so that all of the freshmen are standing next to each other?

 May 23, 2024

Best Answer 

 #1
avatar+1926 
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The freshmen are able to stand in 4! = 24 ways. There are 4 ways we can put them into the line with them all standing together. 

The sohphomores can staned in 3! = 6. 

 

We just have to do 24*4*6 = 576. 

 

There are 576 ways we could arrange them!

 

Thanks! :)

 May 23, 2024
 #1
avatar+1926 
0
Best Answer

The freshmen are able to stand in 4! = 24 ways. There are 4 ways we can put them into the line with them all standing together. 

The sohphomores can staned in 3! = 6. 

 

We just have to do 24*4*6 = 576. 

 

There are 576 ways we could arrange them!

 

Thanks! :)

NotThatSmart May 23, 2024

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