A committee of 4 students is to be selected from 6 boys and 5 girls. In how many ways can the committee be formed if it must contain at least 2 girls?
Answer and explanation
Correct answer: A.
Case 1: Exactly 2 girls and 2 boys,
Case 2: Exactly 3 girls and 1 boy,
Case 3: Exactly 4 girls and 0 boys.
Case 1: ,
Case 2: ,
Case 3: .
.
Case 2: Exactly 3 girls and 1 boy,
Case 3: Exactly 4 girls and 0 boys.
Case 1: ,
Case 2: ,
Case 3: .
.
- Step 1: Partition the requirement of "at least 2 girls" into three mutually exclusive cases based on the number of girls in the 4-student committee :
- Step 2: Calculate the number of combinations for each case using combinations :
- Step 3: Sum the ways across all disjoint cases :
Answer
.
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