Our club has 10 members, and wishes to pick a president, secretary, treasurer, morale officer, and dog catcher. In how many ways can we choose the officers, if individual members can only hold at most one office?
10 ways to pick pres
9 ways to pick secretary
8 ways to pick treasurer
7 ways to pick morale officer
6 ways to pick dog catcher
I think you must of meant "..no person can hold 'more than' 1 office..."
This is the case of the number of "different" ways to select 4 items out of 10.
where the order matters (who holds the president office matters) and no repetition is allowed. This is a permutation problem
so there are 10 choices for president
then after that there are 9 choices for VP
then afte P and VP there are 8 choices for Treasurer
and finally after P, VP and T, there are 7 choices left for Secretary.
So the number of ways to fill those offices with 10 candidates is