You can put this solution on YOUR website! Yes, this is the ONLY differentiating factor between a permutation and a combination; that is , does order matter?
In a permutation, order matters.
In a combination, order does not matter.
Being that the problem says "arranging", this leads one to assume order matters, hence a permutation. If the problem had read "Place 15 DVD's on a shelf", order would not matter, therefore it would have been a combination.