There is a group of 5 seniors and 8 first year graduate students to fill the openings of local news reporters. suppose that we pick 4 students, who are randomly picked from this pool for interviews. using this given information, calculate the following:

1.) find the probability that at least 2 first year graduate students are among the chosen group. note that this is a combinatorics problem and the answer can be left in terms of c k,n. show all work.

Step-by-step explanation:

The total amount of students in the pool is 13.

1) Find the probability that at least 2 first year graduate students are among the chosen group.

The total amount of different ways to chose 4 students from a pool of 13 is

The total amount of ways to choose at least 2 first year graduate students would be:

Ways of choose 2 first year students and 2 seniors + ways of choose 3 first year students and 1 senior + ways of choose 4 first year students. (we are adding and not multiplying because it's "choose 2 first year OR 3 OR 4")

Therefore, the probability would be:

Simplifying x + 7.05 = 45.3 reorder the terms: 7.05 + x = 45.3 solving 7.05 + x = 45.3 solving for variable 'x'. move all terms containing x to the left, all other terms to the right. add '-7.05' to each side of the equation. 7.05 + -7.05 + x = 45.3 + -7.05 combine like terms: 7.05 + -7.05 = 0.00 0.00 + x = 45.3 + -7.05 x = 45.3 + -7.05 combine like terms: 45.3 + -7.05 = 38.25 x = 38.25 simplifying x = 38.25