Q:

Saved Required information NOTE: This is a multi-part . Once an answer is submitted, you will be unable to return to this part A club has 28 members. How many ways are there to choose a president, vice president, secretary, and treasurer of the club, where no person can hold more than one office? Numeric Response

Accepted Solution

A:
Answer: 491400Step-by-step explanation:Given : Total number of members in the club = 28The number of positions = 4Since 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.