Answer: 491400
Step-by-step explanation:
Given : Total number of members in the club = 28
The number of positions = 4
Since no person can hold more than one office, so order matters here.
Therefore, we use permutations to find the number of ways are there to choose given 4 position holders.
The permutation of n things taken r at a time is given by :-
[tex]^nP_r=\dfrac{n!}{(n-r)!}[/tex]
Then , the permutation of 28 things taken 4 at a time is given by :-
[tex]^{28}P_4=\dfrac{28!}{(28-4)!}=\dfrac{28\tiimes27\times26\times25\times24!}{24!}=491400[/tex]
Hence, there are 491400 ways to choose a president, vice president, secretary, and treasurer of the club.
