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How Many Different Committees of 5 Can Be Formed from 6 Men and 4 Women on Which Exact 3 Men and 2 Women Serve?(A) 6(B) 20(C) 60(D) 120 - Mathematics

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MCQ

How many different committees of 5 can be formed from 6 men and 4 women on which exact 3 men and 2 women serve?
(a) 6
(b) 20
(c) 60
(d) 120

Options

  • 6

  • 20

  • 60

  • 120

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Solution

120

\[\text{Number of committes that can be formed} = {}^6 C_3 \times {}^4 C_2 \]
\[ = \frac{6!}{3! 3!} \times \frac{4!}{2! 2!} \]
\[ = \frac{6 \times 5 \times 4}{3 \times 2} \times \frac{4 \times 3}{2} \]
\[ = 120\]

Concept: Combination
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Q 20 | Page 26

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