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?
We can choose 4 of 15 members and permute each set of these in 4! ways
P (15 , 4) *4! =
P VP S T
15 x 14 x 13 x 12
15x14x13x12=32760, as CPHILL says.