Question
From a group of 8 girls and 7 boys, a committee of 9 is
to be formed. In how many ways can the committee be formed if it must include at least 6 girls?Solution
Case I: 6 girls and 3 boys
Number of ways = 8C6 × 7C3 = 28 × 35 = 980 ways
Case II: 7 girls and 2 boys
Number of ways = 8C7 × 7C2 = 8 × 21 = 168 ways
Case III: 8 girls and 1 boy
Number of ways = 8C8 × 7C1 = 1 × 7 = 7 ways
Total number of ways = 980 + 168 + 7 = 1155 ways
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