Permutations and CombinationsMCQPYQ Nov. 18Question 1613 of 251
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The number of words from the letters of the word BHARAT, in which B and H will never come together, is

Options

A360
B240
C120
DNone of these
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Correct Answer

✅ Option b — 240

All Options:

  • A360
  • B240
  • C120
  • DNone of these

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Detailed Solution & Explanation

Let us analyze the letters of the word **BHARAT**:
- Total letters = 6 (B, H, A, R, A, T).
- Repetition: 'A' appears 2 times.

1. **Total number of arrangements:** The number of ways to arrange the 6 letters is:
textTotalarrangements=frac6!2!=frac7202=360\\text{Total arrangements} = \\frac{6!}{2!} = \\frac{720}{2} = 360
2. **Arrangements where B and H are always together:**
- Treat (BH) as a single block. We now have 5 items: (BH), A, R, A, T.
- The number of ways to arrange these 5 items (where A is repeated 2 times) is:
frac5!2!=frac1202=60textways\\frac{5!}{2!} = \\frac{120}{2} = 60 \\text{ ways}
- Within the block (BH), the letters B and H can arrange themselves in 2!=2\displaystyle 2! = 2 ways (BH or HB).
- Therefore, the number of arrangements where B and H are together is:
textTogether=60times2=120\\text{Together} = 60 \\times 2 = 120
3. **Arrangements where B and H never come together:**
textNevertogether=textTotal−textTogether=360−120=240\\text{Never together} = \\text{Total} - \\text{Together} = 360 - 120 = 240
This matches Option B.
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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