Permutations and CombinationsMCQMTP June 22Question 1658 of 251
All Questions

In how many ways can the letters of the word "ALGEBRA" be arranged without changing the relative order of the vowels?

Options

A82
B70
C72
DNone of these
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option c — 72

All Options:

  • A82
  • B70
  • C72
  • DNone of these

Ad

Detailed Solution & Explanation

The word is ALGEBRA, which contains 7 letters in total:
- Vowels: {A,E,A}\displaystyle \{A, E, A\} (3 vowels, with A\displaystyle A repeating 2 times)
- Consonants: {L,G,B,R}\displaystyle \{L, G, B, R\} (4 distinct consonants)
The original positions of the vowels in the word ALGEBRA are 1st, 4th, and 7th places.
The phrase "without changing the relative order of the vowels" in standard CA Foundation questions means that the vowel positions remain fixed (i.e., vowels occupy the 1st, 4th, and 7th positions, while consonants occupy the 2nd, 3rd, 5th, and 6th positions).
1. Arrange the vowels {A,E,A}\displaystyle \{A, E, A\} in the 3 fixed vowel positions:
Ways=3!2!=3 ways\text{Ways} = \frac{3!}{2!} = 3 \text{ ways}
2. Arrange the 4 distinct consonants {L,G,B,R}\displaystyle \{L, G, B, R\} in the 4 fixed consonant positions:
Ways=4!=24 ways\text{Ways} = 4! = 24 \text{ ways}
Using the multiplication principle, the total number of ways is:
Total=3×24=72 ways\text{Total} = 3 \times 24 = 72 \text{ ways}
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

More Questions from Permutations and Combinations

The value of N\displaystyle N in N!+17!=18!\displaystyle N! + \frac{1}{7!} = \frac{1}{8!} is

A person can go from place 'A' to 'B' by 11 different modes of transport but is allowed to return to 'A' by any mode other than the one earlier. The number of different ways in which the entire journey can be completed is:

If a man travels from place A to B in 10 ways then by how many ways can he come back by another train?

If n!10(n−1)!=(n−1)!(n−3)!\displaystyle \frac{n!}{10(n-1)!} = \frac{(n-1)!}{(n-3)!} find 'n'.

Which of the following is a correct statement.

nP3=2⋅nP2\displaystyle ^nP_3 = 2 \cdot ^nP_2. Find n\displaystyle n.

Ready to Master Permutations and Combinations?

Practice all 251 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free