The president can be any of the seven members, so there are 7 choices for president.
The vice president can be any of the remaining six members (since the president cannot also be the vice president), so there are 6 choices for vice president.
The secretary-treasurer can be any of the remaining five members, so there are 5 choices for secretary-treasurer.
Therefore, the total number of ways to choose the three officers is $7\times6\times5=\boxed{210}$.
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 filled.
1 answer