The main difference between permutations and combinations depends on order. Permutation refers to the arrangement of a number of objects. For example, if we're arranging notebooks on a bookshelf, mainly the order in which they are placed matters, and thus, it is a permutation problem. On the other hand, for Combination, we refer to selecting objects without the order. If we're selecting a group from a crowd, the arrangement doesn’t matter, only the selection does, thus it makes it a combination problem.