which one? permutation or combination?

Question

Let say we have a bookshelf that can fit 6 books, we want 4 computer science books and 2 physics books but computer books should be together and physics books also should be together, we have 8 computer and 6 physics book in total in how many ways we can do that?

I believe that the answer is like this:

c(8,4)*c(6,2) + c(6,2)*c(8,4)

but my instructor sloved it in this way(by p I mean permutation):

p(8,4)*p(6,2) + p(6,2)*p(8,4)

could u please tell me which one is right?

Answer 1

Your answer is correct if you don't care what order the books go on the shelf. Your instructor's answer is correct if you count different orderings of the books within each of the two groups as different ways of filling the bookshelf.