Answer:
2730 ways
Step-by-step explanation:
Given that,
There are 15 eligible candidates for these positions.
The newly elected president needs to decide the remaining 3 spots available in the cabinet he/she is appointing.
It is a concept based on permutations.
[tex]P(n,r)=\dfrac{n!}{(n-r)!}[/tex]
Put n = 15 and r = 3
[tex]P(15,3)=\dfrac{15!}{(15-3)!}\\\\=\dfrac{15!}{12!}\\\\=\dfrac{15\times 14\times 13\times 12!}{12!}\\\\=15\times 14\times 13\\\\=2730[/tex]
Hence, 2730 ways can the members of the cabinet be appointed
