Mathematics · Permutations and Combinations

JEE Main 2024 — 4 April, Shift 2 — Question 26

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

Numerical answer — enter this value.

Step-by-step solution

From Group A	From Group B	Ways of selection
4 M	4 W	${{~}^{4}}{{\text{C}}_{4}}{{~}^{4}}{{\text{C}}_{4}}=1$
3 M 1 W	1 M 3 W	${{~}^{4}}{{\text{C}}_{3}}{{~}^{5}}{{\text{C}}_{1}}{{~}^{5}}{{\text{C}}_{1}}{{~}^{4}}{{\text{C}}_{3}}=400$
2 M 2 W	2 M 2 W	${{~}^{4}}{{\text{C}}_{2}}{{~}^{5}}{{\text{C}}_{2}}{{~}^{5}}{{\text{C}}_{2}}{{~}^{4}}{{\text{C}}_{2}}=3600$
1 M 3 W	3 M 1 W	${{~}^{4}}{{\text{C}}_{1}}{{~}^{5}}{{\text{C}}_{3}}{{~}^{5}}{{\text{C}}_{3}}{{~}^{4}}{{\text{C}}_{1}}=1600$
4 W	4 M	${{~}^{5}}{{\text{C}}_{4}}{{~}^{5}}{{\text{C}}_{4}}=25$
Total	5626

Ans. 5626

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 4 April, Shift 2
Subject: Mathematics
Chapter: Permutations and Combinations
Topic: Combinations