Question

There are 4 men and 5 women in Group A, and 5 men and 4 women in Group B. If 4 persons are selected from each group, then the number of ways of selecting 4 men and 4 women is

Answer 1

We need to select 4 men (M) and 4 women (W) from the two groups. Consider the following cases:

$\text{From Group A}$	$\text{From Group B}$	$\text{Ways of Selection}$
4M	4W	${{4}\choose{4}} \cdot {{4}\choose{4}} = 1$
3M1W	1M3W	${{4}\choose{3}} \cdot {{5}\choose{1}} \cdot {{5}\choose{3}} \cdot {{4}\choose{1}} = 400$
2M2W	2M2W	${{4}\choose{2}} \cdot {{5}\choose{2}} \cdot {{5}\choose{2}} \cdot {{4}\choose{2}} = 3600$
1M3W	3M1W	${{4}\choose{1}} \cdot {{5}\choose{3}} \cdot {{5}\choose{1}} \cdot {{4}\choose{3}} = 1600$
4W	4M	${{5}\choose{4}} \cdot {{5}\choose{4}} = 25$
Total	5626

Final Answer: 5626.