Question 746985
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.