Question
In a Group of 8 boys and 6 girls, Six children are to be
selected. In how many different ways can they be selected such that at least one boy should be there?Solution
For At least 1 boy we have (1 boy and 5 girls), (2 boys and 4 girls), (3 boys and 3 girls), (4 boys and 2 girls), (5 boys and 1 girl), (6 boys) ∴ Required Number of ways = (8C1 × 6C5) + (8C2 × 6C4) + (8C3 × 6C3) + (8C4 × 6C2) + (8C5 × 6C1) + 8C6 = 48 + 420 + 1120 + 1050 + 336 + 28 = 3002 ways
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