Question

Consider a school with two classes, A and B. In class A there are 15 girls and 17 boys. In class B, there are 19 girls and 10 boys. Both classes plan extracurricular activities for which each class forms a committee consisting of three students. How many possible committees are there such that the total of committee members of both classes combined consists of 4 girls

Answer 1

Answer: 7700 committee

Explanation:

Given that In class A there are 15 girls and 17 boys. And In class B, there are 19 girls and 10 boys

To find possible committees of 3 such that the total of committee members of both classes combined consists of 4 girls, we will use combination technique

(15C2 × 17C1) + (19C2 × 10C1)

Or

(15C1× 17C2) + (19C3 ×10C0)

Or

(15C3 × 17C0) + (19C1 × 10C2)

Note that "or" means addition

(1785 + 1710) + (2040 + 855) + (455 + 855)

= 3495 + 2895 + 1310

= 7700 committee