Respuesta :
Answer:
The members of the cabinet can be appointed in 121,080,960 different ways.
Step-by-step explanation:
The rank is important(matters), which means that the order in which the candidates are chosen is important. That is, if we exchange the position of two candidates, it is a new outcome. So we use the permutations formula to solve this quesiton.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
If there are 14 eligible candidates for these positions (where rank matters), how many different ways can the members of the cabinet be appointed?
Permutations of 8 from a set of 14. So
[tex]P_{(14,8)} = \frac{14!}{(14-8)!} = 121,080,960[/tex]
The members of the cabinet can be appointed in 121,080,960 different ways.
