Respuesta :
Using permutations and the probability concept, it is found that there is a 0.0417 = 4.17% probability that Nia is chosen as president.
- A probability is the number of desired outcomes divided by the number of total outcomes.
- As there are different roles, the order in which the students are chosen is important, hence, the permutation formula is used to solve this question.
Permutation formula:
The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
Desired outcomes:
- Nia's president.
- For the other roles, 3 students from a set of 23, hence:
[tex]D = P_{23,3} = \frac{23!}{20!} = 10626[/tex]
Total outcomes:
4 students from a set of 24, hence:
[tex]T = P_{24,4} = \frac{24!}{20!} = 255024[/tex]
Then:
[tex]p = \frac{D}{T} = \frac{10626}{255024} = 0.0417[/tex]
0.0417 = 4.17% probability that Nia is chosen as president.
To learn more about probabilities, you can take a look at https://brainly.com/question/24437717
