You can put this solution on YOUR website!
a club with 10 members is to pick a president, vice president, treasurer, and secretary. If each office is to be held by one person and no person can hold 1 offices, in how many ways can those offices be filled?
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