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:

a

step-by-step explanation:

1. 180°. the sum of the interior angles of a triangle is 180°, for the equilateral triangle that it has three equals side is 60°+60°+60°=180°.

2. 60°. each interior angle of a equilateral triangle is 60°

3. 120°. the measure of ∠m is 120°, the sum of the angles ∠m and ∠n is equal to 180°. so, in order to find the measure of ∠m, we have ∠m+∠n=180° > ∠m=180°-∠n > ∠m=180°-60°=120°.

4. 360°. the sum of the exterior angles of an equilateral triangle is ∠m+∠r+∠x=120°+120°+120°=360°. the exterior angles of any triangle always add 360°.