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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 the freshmen are standing together?

 Dec 23, 2023
 #1
avatar+126665 
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The sophomores  can  occupy  any of  4  positions

And the can  be arranged in 4! = 24 ways

And for each of these the sophomores can be arranged in 3!  = 6 ways

 

So

 

4 * 24 * 6  =   576  ways

 

cool cool cool

 Dec 24, 2023

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