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?
I think its 5
The freshmen can occupy any 4 positions
And for each of these they can be arranged in 4! = 24 ways
And the sophomores can occupy any of the other 3 positions and can be arranged in 3! = 6 ways
So
4 * 24 * 6 =
576 arrangements
+1678 
