How many different committees of 5 can be formed from 6 men and 4 women on which exact 3 men and 2 women serve?

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

Solution:

(d) 120

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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