A club with seven members is to choose three officers: president, vice president, and secretary-treasurer. If each office is to be held by one person and no person can hold more than one office, in how many ways can those offices be held.
There are 7 options for the first office, since any of the 7 members can become president. After a member is chosen as president, there are 6 remaining options for vice president, and after both president and vice president are chosen, there are 5 remaining options for secretary-treasurer. So there are $7 \cdot 6 \cdot 5 = \boxed{210}$ ways to choose the officers.
