JEE MAIN - Mathematics (2024 - 4th April Evening Shift - No. 30)
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
5626
Explanation
| Group A | Group B | Ways |
|---|---|---|
| $$4m$$ $$3m+1w$$ $$2m+2w$$ $$1m+3w$$ $$4w$$ |
$$4w$$ $$1m+3w$$ $$2m+2w$$ $$3m+w$$ $$4m$$ |
$${ }^4 C_4 \cdot{ }^4 C_4 \quad=1$$ $${ }^4 C_1 \cdot{ }^5 C_1 \cdot{ }^5 C_1^4 C_3 \quad=400$$ $${ }^4 C_2 \cdot{ }^5 C_2{ }^5 C_2{ }^4 C_2 \quad=3600$$ $${ }^4 C_1{ }^5 C_3{ }^5 C_3{ }^4 C_1 \quad=1600$$ $${ }^5 C_4{ }^5 C_4 \quad=25$$ |
$$\begin{aligned} \text { Total ways } & =1+400+3600+1600+25 \\ & =5626 \end{aligned}$$
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