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:

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

The members of the cabinet can be appointed in 121,080,960 different ways.
Answer:
There are 40 musicians that are only marching band.
Step-by-step explanation:
Since we knot that there are 25 musicians that do both that means there is 60 - 25 = 35 musicians who do only jazz band. From his we can answer the question because....
100 = a + b + c
Where "a" is the number of musicians who go only to jazz, "b" is the number of people who do both, and "c" is the number of people that go only to the marching band. From here we can do this....
100 = a + b + c
c = 100 - a - b
Substitute the value we found outa and get.....
c = 100 - 35 - 25
c = 40
The symbol ₁₂P₉ represents the permutations of 9 quantities out of 12.
By definition,

From the calculator,
12! = 479,001,600
3! = 6
Therefore
₁₂P₉ = 479001600/6 = 79,833,600
Answer: 79,833,600
D- 4 is your correct answer :)
Hope this helps