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?
I need to assign three distinct roles to three distinct people, so order matters. This means I can use the multiplication principle: for each choice of president, I have two choices for secretary, and then one choice for treasurer. So the total number of ways to choose the officers is 3 x 2 x 1, which is 6. Another way to think about this is that I am permuting three objects, so I can use the formula for permutations: P(3,3) = 3! = 6. 