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…

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 _____

Solution

$\begin{array}{|l|l|l|} \hline {\begin{array}{c} \text{From} \\ \text{Group A} \end{array}} & {\begin{array}{c} \text{From} \\ \text{Group B} \end{array}} & \text{Ways of selection} \\ \hline 4 \mathrm{M} & 4 \mathrm{~W} & { }^4 \mathrm{C}_4{ }^4 \mathrm{C}_4=1 \\ \hline 3 \mathrm{M} 1 \mathrm{~W} & 1 \mathrm{M} 3 \mathrm{~W} & { }^4 \mathrm{C}_3{ }^5 \mathrm{C}_1{ }^5 \mathrm{C}_1{ }^4 \mathrm{C}_3=400 \\ \hline 2 \mathrm{M} 2 \mathrm{~W} & 2 \mathrm{M} 2 \mathrm{~W} & { }^4 \mathrm{C}_2{ }^5 \mathrm{C}_2{ }^5 \mathrm{C}_2{ }^4 \mathrm{C}_2=3600 \\ \hline 1 \mathrm{M} 3 \mathrm{~W} & 3 \mathrm{M} 1 \mathrm{~W} & { }^4 \mathrm{C}_1{ }^5 \mathrm{C}_3{ }^5 \mathrm{C}_3{ }^4 \mathrm{C}_1=1600 \\ \hline 4 \mathrm{~W} & 4 \mathrm{M} & { }^5 \mathrm{C}_4{ }^5 \mathrm{C}_4=25 \\ \hline \text{ Total } & \text{5626} \\ \hline \end{array}$

Asked in: JEE Main 2024 (04 Apr Shift 2)

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