Permutations and CombinationsPYQ Sept 25Question 4426 of 183
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In a school, for a class monitor selection, there are 6 candidates, and students need to choose up to 3 monitors. A student can vote for 1 or 2 or 3 candidates. In how many ways a student can vote?

Options

A41
B42
C43
D44
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Correct Answer

✅ Option a — 41

All Options:

  • A41
  • B42
  • C43
  • D44

Detailed Solution & Explanation

There are 6 candidates. A student can choose to vote for 1, 2, or 3 candidates.
Let us calculate the number of ways for each case: 1) Voting for 1 candidate out of 6: 6C1=6 ways^6C_1 = 6\text{ ways}
2) Voting for 2 candidates out of 6: 6C2=6×52×1=15 ways^6C_2 = \frac{6 \times 5}{2 \times 1} = 15\text{ ways}
3) Voting for 3 candidates out of 6: 6C3=6×5×43×2×1=20 ways^6C_3 = \frac{6 \times 5 \times 4}{3 \times 2 \times 1} = 20\text{ ways}
Total number of ways a student can vote: Total ways=6C1+6C2+6C3=6+15+20=41 ways\text{Total ways} = ^6C_1 + ^6C_2 + ^6C_3 = 6 + 15 + 20 = 41\text{ ways}
Hence, **Option A** 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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