Permutations and CombinationsMCQPYQ Dec 23Question 1629 of 251
All Questions

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

Options

A810
B1440
C25200
D50400
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option d — 50400

All Options:

  • A810
  • B1440
  • C25200
  • D50400

Ad

Detailed Solution & Explanation

Let us analyze the letters of the word **CORPORATION**:
- Total letters = 11.
- Vowels = O, O, A, I, O (5 vowels: three O's, one A, one I).
- Consonants = C, R, P, R, T, N (6 consonants: one C, two R's, one P, one T, one N).

Since the vowels must always come together:
1. **Treat the vowels as a single block:** (OOAIO). We now have 7 items to arrange: the block (OOAIO) and the 6 consonants.
2. **Arrange the 7 items:** Since R is repeated 2 times among the consonants, the number of ways to arrange these 7 items is:
frac7!2!=frac50402=2520textways\\frac{7!}{2!} = \\frac{5040}{2} = 2520 \\text{ ways}
3. **Arrange the vowels within the block:** The 5 vowels (O, O, A, I, O) have three O's. The number of ways to arrange them is:
frac5!3!=frac1206=20textways\\frac{5!}{3!} = \\frac{120}{6} = 20 \\text{ ways}
4. **Total arrangements:** By the multiplication principle, the total number of ways is:
textTotalways=frac7!2!timesfrac5!3!=2520times20=50,400\\text{Total ways} = \\frac{7!}{2!} \\times \\frac{5!}{3!} = 2520 \\times 20 = 50,400
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.

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