Question

Find number of ways of arranging 4 Boys \& 3 Girls such that all girls are not together :

• A. 4430
• B. 4445
• C. 4320
• D. 4431

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
"All girls are not together" means we subtract the cases where all girls are together from the total possible arrangements.
Step 2: Key Formula or Approach:
1. Total arrangements of $n$ distinct objects is $n!$.
2. To find arrangements where specific objects are together, treat them as a single unit (String method).
Step 3: Detailed Explanation:
1. Total people $= 4 + 3 = 7$.
Total arrangements $= 7! = 5040$.
2. Arrange such that all 3 girls are together:
Treat the 3 girls as 1 single block.
Remaining units $= 4 \text{ boys} + 1 \text{ girl-block} = 5$ units.
Arrangement of these 5 units $= 5! = 120$.
Internal arrangement of 3 girls within the block $= 3! = 6$.
Total "girls together" arrangements $= 120 \times 6 = 720$.
3. "All girls not together" $=$ Total $-$ Girls together:
$5040 - 720 = 4320$.
Step 4: Final Answer:
The number of ways is 4320.