Question

A group of students comprises 5 boys and n girls. If the number of ways, in which a team of 3 students can randomly be selected from this group such that there is at least one boy and at least one girl in each team, is 1750, then n is equal to_____

A. 25
B. 28
C. 27
D. 24

Answer 1

By calculating combinations for selecting a team of 3 students from a group comprised of 5 boys and n girls such that the team must have at least one boy and one girl, and setting the resultant equation equal to 1750, we find that n equals 27. Through these calculations, we find that n is equal to 27, which is option C.

Step-by-step explanation:

The subject of this question is mathematics, specifically involving combinatorics and the concept of hypergeometric distribution. A hypergeometric problem arises when we choose from two groups without replacement and have a specific group of interest.

To find the number of girls, n, in a group of students where the total number of ways to select a team of 3 students that includes at least one boy and one girl is 1750, we must compute the different combinations that satisfy this condition.

We can choose 2 boys and 1 girl or 1 boy and 2 girls. Calculating these combinations and setting their sum to 1750, we can find the value of n. The combinations we calculate are:

1. C(5,2) × C(n,1) for 2 boys and 1 girl
2. C(5,1) × C(n,2) for 1 boy and 2 girls

Through these calculations, we find that n is equal to 27, which is option C.