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In how many ways a committee consisting of 5 men and 6 women can be formed from 8 men and 10 women?
1. 5041
2. 5040
3. 11670
4. 11760

1 Answer

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Correct Answer - Option 4 : 11760

Calculation:

The committee can be formed in 8C5 × 10C6 ways

⇒ {8!/5! × (8 - 5)!} × {10!/6! × (10 - 6)!}

⇒ {8!/5! × 3!} × {10!/6! × 4!}

⇒ {(8 × 7 × 6)/(3 × 2 × 1)} × {(10 × 9 × 8 × 7)/(4 × 3 × 2 × 1)}

⇒ (8 × 7) × (10 × 3 × 7)

⇒ 11760

∴ The committee can be formed in 11760 ways.

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