Final answer:
To form a committee of 5 members from a group of 6 boys and 4 girls with at most 2 girls, we consider different scenarios and sum the combinations: no girls, 1 girl, and 2 girls. We calculate this using the combination formula and add the results of each scenario. c) C(6,4)×C(4,1) is correct answer.
Step-by-step explanation:
The question asks us to find out in how many ways we can form a committee of 5 members from 6 boys and 4 girls if at most 2 girls are included. This scenario requires using the combination formula, which is written as C(n, r) and calculates the number of ways to choose r elements from a set of n without regard to the order of selection.
We can have the following scenarios for the committee formation:
- No girls: All 5 members will be boys. We choose 5 out of 6 boys, which is C(6, 5).
- 1 girl: We choose 1 out of 4 girls and 4 out of 6 boys, which is C(4, 1) × C(6, 4).
- 2 girls: We choose 2 out of 4 girls and 3 out of 6 boys, which is C(4, 2) × C(6, 3).
The total number of ways to form the committee is the sum of the number of ways for each scenario:
C(6, 5) + C(4, 1) × C(6, 4) + C(4, 2) × C(6, 3)