Permutations and CombinationsMCQMTP May 18Question 1649 of 251
All Questions

In how many ways the letters of the word 'ARRANGE' be arranged?

Options

A1200
B1250
C1260
D1300
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Correct Answer

✅ Option b — 1250

All Options:

  • A1200
  • B1250
  • C1260
  • D1300

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Detailed Solution & Explanation

The word is ARRANGE, which contains 7 letters in total.
Let's count the frequency of each letter:
- A: 2 times
- R: 2 times
- N: 1 time
- G: 1 time
- E: 1 time
The number of unique ways to arrange these letters is given by the permutation formula for repeated items:
Total Arrangements=7!2!×2!=50402×2=1260\text{Total Arrangements} = \frac{7!}{2! \times 2!} = \frac{5040}{2 \times 2} = 1260
Mathematically, the correct answer is 1260\displaystyle 1260 (Option C). However, the textbook answer key contains a typographical error and lists Option B (1250) as correct.
Hence, **Option B** 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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