Permutations and CombinationsMCQMTP Dec 2023 Series IIQuestion 1739 of 249
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A Supreme Court Bench consists of 5 judges. In how many ways, the bench can give a majority decision?

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option d — 16

All Options:

  • A10
  • B5
  • C15
  • D16

Detailed Solution & Explanation

A Supreme Court Bench consists of 5\displaystyle 5 judges. A majority decision requires **at least 3 judges** to agree on the decision.

This means the majority can be formed by:
1. Exactly 3\displaystyle 3 judges
2. Exactly 4\displaystyle 4 judges
3. Exactly 5\displaystyle 5 judges

Let us calculate the number of ways to choose these judges:
- Choosing 3\displaystyle 3 judges out of 5\displaystyle 5:
5C3=5×42×1=10 ways^{5}C_{3} = 5×42×1=10\displaystyle \frac{5 \times 4}{2 \times 1} = 10  ways\displaystyle \text{ ways}
- Choosing 4\displaystyle 4 judges out of 5\displaystyle 5:
5C4=5 ways^{5}C_{4} = 5  ways\displaystyle \text{ ways}
- Choosing 5\displaystyle 5 judges out of 5\displaystyle 5:
5C5=1 way^{5}C_{5} = 1  way\displaystyle \text{ way}
Summing these up, the total number of ways the bench can give a majority decision in favor of an opinion is:
Total Ways=5C3+5C4+5C5Total Ways=5C3+5C4+5C5\displaystyle \text{Total Ways} = ^{5}C_{3} + ^{5}C_{4} + ^{5}C_{5}
Total Ways=10+5+1=16Total Ways=10+5+1=16\displaystyle \text{Total Ways} = 10 + 5 + 1 = 16

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

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