Permutations and CombinationsMCQPYQ Dec. 21Question 1616 of 251
All Questions

The number of words that can be formed using the letters of the "PETROL" such that the words do not have "P" in the first position, is

Options

A720
B120
C600
D240
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Correct Answer

✅ Option c — 600

All Options:

  • A720
  • B120
  • C600
  • D240

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Detailed Solution & Explanation

Let us solve the problem step-by-step using permutations:
The letters of the word **PETROL** are: P, E, T, R, O, L (6 distinct letters).

1. **Total possible permutations:** The number of ways to arrange 6 distinct letters is:
textTotal=6!=720\\text{Total} = 6! = 720
2. **Permutations starting with P:** If we place P in the first position (1 choice), the remaining 5 letters can be arranged in the remaining 5 positions in:
textStartingwithP=5!=120\\text{Starting with P} = 5! = 120
3. **Permutations not starting with P:** The number of words that do not have P in the first position is:
textNotstartingwithP=textTotal−textStartingwithP\\text{Not starting with P} = \\text{Total} - \\text{Starting with P}
textNotstartingwithP=720−120=600\\text{Not starting with P} = 720 - 120 = 600
This mathematically correct value (600) corresponds to Option C. However, the textbook key incorrectly lists Option B (120) as correct, which is the number of words that *do* start with P. We proceed with the correct mathematical derivation.
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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