Mathematics · Permutations and Combinations

JEE Main 2025 — 24 January, Evening Shift — Question 14

Group $A$ consists of 7 boys and 3 girls, while group $B$ consists of 6 boys and 5 girls. The number of ways, 4 boys and 4 girls can be invited for a picnic if 5 of them must be from group A and the remaining 3 from group $B$ , is equal to:

Option A:
8575
Option B:
9100
Option C:
8925
Correct
Option D:
8750

Answer: C

Step-by-step solution

Total $=\mathrm{C}-\mathrm{I}+\mathrm{C}-\mathrm{II}+\mathrm{C}-\mathrm{III}$

$={ }^{7} \mathrm{C}_{2} \cdot{ }^{3} \mathrm{C}_{3} \cdot{ }^{6} \mathrm{C}_{2} \cdot{ }^{5} \mathrm{C}_{1}+{ }^{7} \mathrm{C}_{3} \cdot{ }^{3} \mathrm{C}_{2} \cdot{ }^{6} \mathrm{C}_{1}{ }^{5} \mathrm{C}_{2}+{ }^{7} \mathrm{C}_{4} \cdot{ }^{3} \mathrm{C}_{1} \cdot{ }^{6} \mathrm{C}_{0} \cdot{ }^{5} \mathrm{C}_{3}$

$=8925$

Answer key and solution verified before publishing.

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Exam: JEE Main 2025
Paper: 24 January, Evening Shift
Subject: Mathematics
Chapter: Permutations and Combinations
Topic: Distribution of Objects into Groups

Number of functions f : \1, 2, ..., 100\ arrow \0, 1\, that assign 1 to exactly one of the positive integers less than or equal to 98, is…

Answer: C

Step-by-step solution

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