Permutations & CombinationsmediumPYQ · JEE Main · 4 Apr 2026 · Shift 1 (Morning)Free

Queue of 4 Boys, 3 Girls Not All Together: 4320 | JEE 2026

JEE Maths question with a full step-by-step solution.

Question
The number of ways of forming a queue of 44 boys and 33 girls such that all the girls are not together, is
A50405040
B30503050
C34103410
D43204320correct
Solution
Step 1: Total arrangements of 77 distinct students =7!=5040=7!=5040. Step 2: Arrangements with all 33 girls together: treat the girls as one block, giving 5!5! arrangements of (4 boys + 1 block), times 3!3! internal arrangements:
5!⋅3!=120⋅6=720.5!\cdot3!=120\cdot6=720.
 Step 3: Girls not all together:
7!−5! 3!=5040−720=4320.7!-5!\,3!=5040-720=4320.
 Correct answer: (4)
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