Permutations and CombinationsMCQMTP May 20Question 1651 of 251
All Questions

The number of ways the letters of the word 'COMPUTER' can be rearranged is

Options

A40,320
B40,319
C40,318
Dnone of these
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Correct Answer

✅ Option b — 40,319

All Options:

  • A40,320
  • B40,319
  • C40,318
  • Dnone of these

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Detailed Solution & Explanation

The word is COMPUTER, which contains 8 distinct letters: {C,O,M,P,U,T,E,R}\displaystyle \{C, O, M, P, U, T, E, R\}.
The total number of ways to arrange these 8 distinct letters is:
Total arrangements=8!=40320\text{Total arrangements} = 8! = 40320
The question asks for the number of ways the letters can be *rearranged*.
"Rearranging" means forming a new, different arrangement other than the original word itself.
Thus, we must subtract the 1 original arrangement (COMPUTER) from the total:
Rearrangements=8!−1=40320−1=40319\text{Rearrangements} = 8! - 1 = 40320 - 1 = 40319
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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