Permutations and CombinationsMCQMTP Nov 19Question 1711 of 251
All Questions

A box contains 7 red, 6 white and 4 blue balls. How many selections of three balls on of each colour?

Options

A178
B158
C198
D168
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Correct Answer

✅ Option d — 168

All Options:

  • A178
  • B158
  • C198
  • D168

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Detailed Solution & Explanation

We want to choose 3 balls, one of each color, from a box containing:
- 7 red balls
- 6 white balls
- 4 blue balls
1. The number of ways to choose 1 red ball from 7 is 7C1=7\displaystyle ^7C_1 = 7.
2. The number of ways to choose 1 white ball from 6 is 6C1=6\displaystyle ^6C_1 = 6.
3. The number of ways to choose 1 blue ball from 4 is 4C1=4\displaystyle ^4C_1 = 4.
Using the multiplication principle, the total number of ways to select the three balls is:
Total=7×6×4=168\text{Total} = 7 \times 6 \times 4 = 168
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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