Permutations and CombinationsMCQPYQ Jun 23Question 1628 of 251
All Questions

In how many different ways can the letters of the word 'SOFTWARE' be arranged so that the vowels always come together?

Options

A720
B1440
C2880
D4320
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Correct Answer

✅ Option d — 4320

All Options:

  • A720
  • B1440
  • C2880
  • D4320

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Detailed Solution & Explanation

Let us solve this problem step-by-step using permutations:
The letters of the word **SOFTWARE** are: S, O, F, T, W, A, R, E (8 distinct letters).
- Vowels = O, A, E (3 vowels).
- Consonants = S, F, T, W, R (5 consonants).

Since the vowels must always come together:
1. **Treat the vowels as a single block:** (OAE). We now have 6 items to arrange: the block (OAE) and the 5 consonants.
2. **Arrange the 6 items:** The number of ways to arrange these 6 items is:
6!=720textways6! = 720 \\text{ ways}
3. **Arrange the vowels within the block:** The 3 vowels within the block (OAE) can be arranged in:
3!=6textways3! = 6 \\text{ ways}
4. **Total arrangements:** By the multiplication principle, the total number of ways is:
textTotalways=6!times3!=720times6=4320\\text{Total ways} = 6! \\times 3! = 720 \\times 6 = 4320
This matches Option D.
Hence, **Option D** 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.

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Permutations vs Combinations: The Quantitative Aptitude Guide

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