Permutations and CombinationsMCQMTP Mar 22/RTP Sep 24Question 1657 of 251
All Questions

The number of ways of arranging 6 boys and 4 girls in a row so that all 4 girls are together is:

Options

A6!4!\displaystyle 6!4!
B2(7!4!)\displaystyle 2(7!4!)
C7!4!\displaystyle 7!4!
D6!(4!)\displaystyle 6!(4!)
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Correct Answer

✅ Option c — 7!4!\displaystyle 7!4!

All Options:

  • A6!4!\displaystyle 6!4!
  • B2(7!4!)\displaystyle 2(7!4!)
  • C7!4!\displaystyle 7!4!
  • D6!(4!)\displaystyle 6!(4!)

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Detailed Solution & Explanation

We need to arrange 6 boys and 4 girls in a row such that all 4 girls are always together.
1. Treat the 4 girls as a single entity/block. This block along with the 6 boys gives us 6+1=7\displaystyle 6 + 1 = 7 entities in total.
Number of ways to arrange these 7 entities in a row = 7!\displaystyle 7! ways.
2. Within the block, the 4 distinct girls can be arranged among themselves in 4!\displaystyle 4! ways.
Therefore, the total number of ways of arranging them is:
Total Ways=7!×4!\text{Total Ways} = 7! \times 4!
Hence, **Option C** is the correct answer.

About This Chapter: Permutations and Combinations

Paper

Paper 3: Quantitative Aptitude

Weightage

4-6 Marks

Key Topics

Factorials, Permutations, Combinations

This chapter deals with the fundamental principles of counting. It covers factorials, circular permutations, restricted permutations, combinations, and the differences between selecting items versus arranging them.

View Official ICAI Syllabus

Exam Strategy Tip

The most common mistake is confusing 'P' (Arrangement) with 'C' (Selection). If order matters (like opening a lock), use P. If order doesn't matter (like choosing a team), use C.

Related Comparison Tables

Permutations vs Combinations: The Quantitative Aptitude Guide

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