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Mathematics · Permutations and Combinations

JEE Main 2026 — 4 April, Morning Shift — Question 31

The number of ways, of forming a queue of 4 boys and 3 girls such that all the girls are not together, is :

  1. Option A:

    5040

  2. Option B:

    3050

  3. Option C:

    3410

  4. Option D:

    4320

    Correct

Answer: D

Step-by-step solution

No. of ways to arrange 7 students =7=7 ! Cases where all girls are together B1 B2 B3 B4G1G2G3=5!3!\mathrm{B}_{1} \mathrm{~B}_{2} \mathrm{~B}_{3} \mathrm{~B}_{4} \mathrm{G}_{1} \mathrm{G}_{2} \mathrm{G}_{3}=5!3! Ans. =7!−5!3!=7!-5!3! =7!−6!=7!-6! =6×6=6 \times 6 ! =6×720=6 \times 720 =4320=4320

Answer key and solution verified before publishing.

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Exam
JEE Main 2026
Paper
4 April, Morning Shift
Subject
Mathematics
Chapter
Permutations and Combinations
Topic
Problems based on both permutations and combinations
The number of ways, of forming a queue of 4 boys and 3 girls such… | JEE Main 2026 PYQ with Solution · DhiX AI