Question
A school wants to form a committee of 5 students from 6
boys and 4 girls. How many ways can the committee be formed if it must contain at least 3 boys?Solution
Case I: 3 boys and 2 girls:
6C3 × 4C2 = 20 × 6 = 120
Case II: 4 boys and 1 girl:
6C4 × 4C1 = 15 × 4 = 60
Case III: 5 boys and 0 girls:
6C5 × 4C0 = 6 × 1 = 6
Total = 120 + 60 + 6 = 186 ways
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