Question
A committee of 5 members is to be formed out of 6 men
and 4 women. In how many ways can a committee consisting of atleast 1 woman be formed?Solution
⁶C₄ × ⁴C₁ + ⁶C₃ × ⁴C₂ + ⁶C₂ × ⁴C₃ + ⁶C₁ × ⁴C₄ = 15 × 4 + 20 × 6 + 15 × 4 + 6 × 1 = 60 + 120 + 60 + 6 = 246 Alternate Method: ¹⁰C₅ - ⁶C₅ = (10 ×9 ×8 ×7 ×6 )/(5 ×4 × 3 × 2) - ⁶C₅ = 252 - ⁶C₅ = 252 – 6 = 246
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