Permutations and CombinationsPYQ May 25Question 4027 of 183
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A team of 3 persons is to be constituted from a group of 2 men and 3 women. In how many ways can this be done if these teams would consist of 1 man and 2 women?

Options

A10
B6
C16
D8
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Correct Answer

✅ Option b — 6

All Options:

  • A10
  • B6
  • C16
  • D8

Detailed Solution & Explanation

We need to form a team of 3 persons consisting of 1 man and 2 women from a group of 2 men and 3 women.
The selection can be done as follows:
1. **Selecting 1 man from 2 men**:
Number of ways = (21)=2\displaystyle \binom{2}{1} = 2

2. **Selecting 2 women from 3 women**:
Number of ways = (32)=3\displaystyle \binom{3}{2} = 3

3. **Total number of ways to form the team**:
By the multiplication principle, the total number of ways is:
Total ways=(21)×(32)=2×3=6\text{Total ways} = \binom{2}{1} \times \binom{3}{2} = 2 \times 3 = 6
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.

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