Respuesta :
Answer:
There are 4,959,360 ways to answer the quiz
Step-by-step explanation:
The number of ways in which we can ranked k people from a group of n is calculated using permutation as:
[tex]nPk=\frac{n!}{(n-k)!}[/tex]
Additionally, the number of ways in which we can choose k people from a group of n is calculated using combinations as:
[tex]nCk=\frac{n!}{k!(n-k)!}[/tex]
So, for the first part we need to ranked 4 influential secretaries-general from a group of 8. it means that we can do that in 1680 ways and it is calculated as:
[tex]8P4=\frac{8!}{(8-4)!}=1680[/tex]
Then for the second part, we need to choose 10 members of the united Nations security council from a group of 15. Now we need to choose at least 2 permanent members so, we have the following options:
1. Choose 2 permanent members and 8 not permanent members. It can be made in 450 ways and it is calculated as:
[tex]5C2*10C8=\frac{5!}{2!(5-2)!}*\frac{10}{8!(10-8)!}=450[/tex]
2. Choose 3 permanent members and 7 not permanent members. It can be made in 1200 ways
[tex]5C3*10C7=\frac{5!}{3!(5-3)!}*\frac{10}{7!(10-7)!}=1200[/tex]
3. Choose 4 permanent members and 6 not permanent members. It can be made in 1050 ways
[tex]5C4*10C6=\frac{5!}{4!(5-4)!}*\frac{10}{6!(10-6)!}=1050[/tex]
4. Choose 5 permanent members and 5 not permanent members. It can be made in 252 ways
[tex]5C5*10C5=\frac{5!}{5!(5-5)!}*\frac{10}{5!(10-5)!}=252[/tex]
So, the number of ways in which we can answer the second part is equal to:
450+1,200+1,050+252=2,952
Finally, the number of ways in which we can answer the quiz is calculated as:
(1,680)*(2,952)=4,959,360
