Permutations and CombinationsMCQMTP Nov 19Question 1710 of 251
All Questions

In how many ways can a group of 3 ladies and four gents be chosen from 8 ladies and 7 gents?

Options

A1950
B1920
C1940
D1960
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Correct Answer

✅ Option d — 1960

All Options:

  • A1950
  • B1920
  • C1940
  • D1960

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Detailed Solution & Explanation

We need to choose a group of 3 ladies and 4 gents from 8 ladies and 7 gents.
1. Choose 3 ladies from 8 ladies:
Ways=8C3=8×7×63×2×1=56 ways\text{Ways} = ^8C_3 = \frac{8 \times 7 \times 6}{3 \times 2 \times 1} = 56 \text{ ways}
2. Choose 4 gents from 7 gents:
Ways=7C4=7C3=7×6×53×2×1=35 ways\text{Ways} = ^7C_4 = ^7C_3 = \frac{7 \times 6 \times 5}{3 \times 2 \times 1} = 35 \text{ ways}
Using the multiplication principle, the total number of ways to choose the group is:
Total=8C3×7C4=56×35=1960\text{Total} = ^8C_3 \times ^7C_4 = 56 \times 35 = 1960
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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