Permutations and CombinationsMCQPYQ June 22Question 1617 of 251
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The no. of different ways the letters of the word "DETAIL" can be arranged in such a way that the vowels can occupy only the odd position is

Options

A32
B36
C48
D60
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Correct Answer

✅ Option b — 36

All Options:

  • A32
  • B36
  • C48
  • D60

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Detailed Solution & Explanation

Let us analyze the letters of the word **DETAIL**:
- Total letters = 6 (D, E, T, A, I, L).
- Vowels = E, A, I (3 vowels).
- Consonants = D, T, L (3 consonants).
- Total positions = 6 (1st, 2nd, 3rd, 4th, 5th, 6th).
- Odd positions = 1st, 3rd, 5th (3 positions).
- Even positions = 2nd, 4th, 6th (3 positions).

The vowels must occupy only the odd positions:
1. Arrange the 3 vowels in the 3 odd positions in 3!=6\displaystyle 3! = 6 ways.
2. Arrange the 3 consonants in the remaining 3 even positions in 3!=6\displaystyle 3! = 6 ways.
3. By the multiplication principle, the total number of ways is:
textTotalways=3!times3!=6times6=36\\text{Total ways} = 3! \\times 3! = 6 \\times 6 = 36
This matches Option B.
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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