A group of n students is assigned seats for each of two classes in the same classroom.How many ways can these seats be assigned if no student is assigned the same seat for both classes?
Okay so this can be done like first I can have $n!$ ways to seat n students in class 1 of the classroom and then when class 2 begins, I make sure these n students sit in $D_n$ ways($D_n$-Derangement of n numbers).
Now initial seating arrangement of $n!$ can be for any one of the two classes.
Hence total ways must be $2 \times n! \times D_n$
Am I Correct?