Permutations and CombinationsMCQMTP Mar 22Question 1656 of 251
All Questions

How many different words can be formed with the letters of the word "LIBERTY"?

Options

A5050
B5040
C5400
D5500
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Correct Answer

✅ Option b — 5040

All Options:

  • A5050
  • B5040
  • C5400
  • D5500

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Detailed Solution & Explanation

The word is LIBERTY, which contains 7 letters: {L,I,B,E,R,T,Y}\displaystyle \{L, I, B, E, R, T, Y\}.
All 7 letters are distinct.
The total number of different words (arrangements) that can be formed using all 7 distinct letters is given by 7!\displaystyle 7!:
Total=7!=7×6×5×4×3×2×1=5040\text{Total} = 7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 5040
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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