Question

At the end of each week, a generous teacher gives some candy to a few randomly selected students. There are 30 studdents in this teacher's class- 16 girls and 14 boys.

a) If the teacher wanted to give candy to 6 of the students, how many possible groups of 6 students can she choose? Answer:

b) To avoid apprearing to favor one gender, the teacher will randomly choose 3 of the 16 girls and 3 of the 14 boys. How many possible groups of 6 can she choose? Answer

c) Find the probability that the teacher gives candy to 3 boys and 3 girls if she chooses 6 students from the class at random. Answer:



quickly need answer. 100 points

Answer 1

The number of possible groups that can be formed is computed using combinations. For six random students, we use C(30, 6). For three girls and three boys, we use C(16, 3) × C(14, 3). Lastly, the probability is found by dividing the number of groups with a balanced gender ratio by the total number of possible groups.

Step-by-step explanation:

The number of possible groups of 6 students that the teacher can choose from 30 students is given by the combination formula C(n, k) = n! / [k!(n-k)!], where n is the total number of students, and k is the number of students to choose.

1. For part a), we have n=30 and k=6, so we calculate C(30, 6).
2. For part b), since the teacher chooses 3 girls out of 16 and 3 boys out of 14, we calculate C(16, 3) × C(14, 3).
3. For part c), the probability that the teacher gives candy to 3 boys and 3 girls is calculated by the formula P(E) = number of favorable outcomes / total number of outcomes. Here, the favorable outcome is the product of C(16, 3) and C(14, 3), and the total outcomes is C(30, 6).