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

Correct Answer: 5626

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.