We have 18 members that can be positioned in 4 positions.
As the positions are different from each other, the order matters.
Then, this is a permutation of 18 elements in 4 places with no repetition.
The number of permutations can be calculated as:
[tex]\begin{gathered} P(n,r)=\frac{n!}{(n-r)!} \\ P(18,4)=\frac{18!}{(18-4)!}=\frac{18!}{14!}=18\cdot17\cdot16\cdot15=73440 \end{gathered}[/tex]We could have derived this by doing this analysis:
We have 18 to choose for captain.
Then, we have 17 left to choose for co-captain.
Finally 16 can be chosen for treasurer and 15 are left for secretary.
Then, the posible teams are 18*17*16*15=73440.
Answer: we can select them in 73,440 ways.
