Permutations and CombinationsMCQMTP Nov 18Question 1707 of 249
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A Company wishes top simultaneously promotes three of its 8 department assistant mangers. In how many ways these promotions can take place?

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

✅ Option a — 336

All Options:

  • A336
  • B56
  • C8
  • D1680

Detailed Solution & Explanation

A company wants to promote 3 of its 8 assistant managers.
1. If the promotions are to 3 identical positions, then we simply choose 3 managers out of 8:
Ways=8C3=8×7×63×2×1=56 ways\displaystyle \text{Ways} = ^8C_3 = \frac{8 ×\displaystyle \times 7 ×\displaystyle \times 6}{3 ×\displaystyle \times 2 ×\displaystyle \times 1} = 56  ways\displaystyle \text{ ways}
This corresponds to Option B.
2. If the promotions are to 3 distinct roles/departments (so that the order in which they are chosen or assigned matters), the number of ways is:
Ways=8P3=8×7×6=336 waysWays=8P3=8\displaystyle \text{Ways} = ^8P_3 = 8 ×\displaystyle \times 7 ×\displaystyle \times 6 = 336  ways\displaystyle \text{ ways}
This corresponds to Option A.
Following the textbook answer key, Option A (336) is marked as correct, assuming the positions are distinct.
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.

Related Comparison Tables

Permutations vs Combinations: The Quantitative Aptitude Guide

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