A political science quiz has two parts. In the first, you must present your opinion of the four most influential secretaries-general in the history of the United Nations in a ranked list. In The second, you must name ten members of the United Nations security council in any order, including at least two permanent members of the council. If there have been eighth secretary general in U. N. history, and there are fifteen members of the U. N. security council, including the five permanent members, how many ways can you answer the quiz, assuming you answer both parts completely

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:

Additionally, the number of ways in which we can choose k people from a group of n is calculated using combinations as:

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:

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:

2. Choose 3 permanent members and 7 not permanent members. It can be made in 1200 ways

3. Choose 4 permanent members and 6 not permanent members. It can be made in 1050 ways

4. Choose 5 permanent members and 5 not permanent members. It can be made in 252 ways

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