My club has 15 members.  In how many ways can we choose a president, vice-president, secretary, and treasurer, if no member can hold more than one office?
There are 15 choices for president, 14 choices for vice-president, 13 choices for secretary, and 12 choices for treasurer, for a total of $15 \times 14 \times 13 \times 12 = \boxed{32,\!760}$ different choices.