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