JEE Main 2024 — Permutation Combination Question with Solution
JEE Main 2024 (04 Apr Shift 2)
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 _____
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Show full solutionCorrect answer: 5626
Correct answer
5626
Step-by-step explanation
$\begin{array}{|l|l|l|}
\hline {\begin{array}{c}
\text{From} \\
\text{Group A}
\end{array}} & {\begin{array}{c}
\text{From} \\
\text{Group B}
\end{array}} & \text{Ways of selection} \\
\hline 4 \mathrm{M} & 4 \mathrm{~W} & { }^4 \mathrm{C}_4{ }^4 \mathrm{C}_4=1 \\
\hline 3 \mathrm{M} 1 \mathrm{~W} & 1 \mathrm{M} 3 \mathrm{~W} & { }^4 \mathrm{C}_3{ }^5 \mathrm{C}_1{ }^5 \mathrm{C}_1{ }^4 \mathrm{C}_3=400 \\
\hline 2 \mathrm{M} 2 \mathrm{~W} & 2 \mathrm{M} 2 \mathrm{~W} & { }^4 \mathrm{C}_2{ }^5 \mathrm{C}_2{ }^5 \mathrm{C}_2{ }^4 \mathrm{C}_2=3600 \\
\hline 1 \mathrm{M} 3 \mathrm{~W} & 3 \mathrm{M} 1 \mathrm{~W} & { }^4 \mathrm{C}_1{ }^5 \mathrm{C}_3{ }^5 \mathrm{C}_3{ }^4 \mathrm{C}_1=1600 \\
\hline 4 \mathrm{~W} & 4 \mathrm{M} & { }^5 \mathrm{C}_4{ }^5 \mathrm{C}_4=25 \\
\hline \text{ Total } & \text{5626} \\
\hline
\end{array}$
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This is a previous-year question from JEE Main 2024, covering the Permutation Combination chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.