What is the Concept of Permutations in Statistics?

[1MileCrash]

In my statistics class I am making use of permutations very often. I need to make sure I understand this.

If I have a set of 13 elements, I can arrange that 13! different ways, because Psub(13,13) = 13!/0!.

If I pick 2 elements from those 13 elements, I can get 13!/11! different results.

Is that what it means?

 

[haruspex]

It depends whether you care about the order of the two picked. If it's an unordered pair, bear in mind that you could have picked the same two in either order.
Imagine the 13 elements in a row, and suppose the leftmost two will be the two picked. There are 13! orderings altogether. For a given pick of two, there are 2!*11! orderings that lead to it. So the number of such pairs is 13!/(2!*11!).