Question

Our club has 25 members, and wishes to pick a president, secretary, and treasurer. In how many ways can we choose the officers, if: (a)individual members can only hold at most one office

Answer 1

Answer:

13800

Step-by-step explanation:

The order of the members is important (because each selected member will receive a different position), thus we then need to use the definition of permutation.

There are 25 members, of which 3 are selected.

$\begin{array}{l}n=25 \\r=3\\end{array}$

Evaluate the definition of a combination:

$P(25,3)=\frac{25 !}{(25-3) !}=\frac{25 !}{22 !}=25 \cdot 24 \cdot 23=13800$