Question:
The number of ways of forming a queue of 4 boys and 3 girls such that all the girls are not together, is:
The number of ways of forming a queue of 4 boys and 3 girls such that all the girls are not together, is:
Updated On: Apr 10, 2026
- 5040
- 3050
- 3410
- 4320
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept:
The phrase "all the girls are not together" means we subtract the cases where all 3 girls form a single block from the total possible arrangements of 7 people.
Step 2: Key Formula or Approach:
Number of ways = (Total arrangements) $-$ (Arrangements where all girls are together).
Step 3: Detailed Explanation:
1. Total arrangements: 7 people can be arranged in $7!$ ways. \[ 7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 5040 \] 2. Girls together: Treat the 3 girls as a single unit (G). Now we have 4 boys + 1 unit = 5 units to arrange. - Number of ways to arrange these 5 units = $5!$. - The 3 girls can be arranged among themselves in $3!$ ways. \[ \text{Together ways} = 5! \times 3! = 120 \times 6 = 720 \] 3. Required ways: \[ 5040 - 720 = 4320 \]
Step 4: Final Answer:
The number of ways is 4320.
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