For 10 point, name this selection in which order matters, unlike combinations.
Groups formed by this sort of operation are subgroups of symmetric groups, notable examples of which include Sylow subgroups.  For any finite group, there is a group of this type to which it is isomorphic according to Cayley's Theorem.  Cycle notation is often used to denote these operations that map a set to itself, examples of which include (*) shuffles.  This operation is also often used to refer to the quantity n!/(n-r)! which is the number of different ways to select r items from a group of n items.  For 10 point, name this selection in which order matters, unlike combinations.
Groups formed by this sort of operation are subgroups of symmetric groups, notable examples of which include Sylow subgroups.  
{Permutation}