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