Given three members of a group -- Alice, Bob, and Carol -- in how many ways can these three be chosen to be the three officers (president, secretary, and treasurer) of the group, assuming no person holds more than one job?
In this problem we are choosing a committee, so the order in which we choose the 3 people does not matter.  We could have chosen them in any of the following orders (where A is Alice, B is Bob, and C is Carol): ABC, ACB, BAC, BCA, CAB, CBA.  So each possible committee corresponds to $3! = \boxed{6}$ possible orderings.