Permutations and CombinationsMCQMTP May 20Question 1665 of 251
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If 12 school teams are participating in a quiz contest, then the number of ways the first, second and third positions may be won is

Options

A1,250
B1,320
C3,210
Dnone of these
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Correct Answer

✅ Option b — 1,320

All Options:

  • A1,250
  • B1,320
  • C3,210
  • Dnone of these

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Detailed Solution & Explanation

To find the number of ways the 1st, 2nd, and 3rd positions can be won among 12 participating school teams, we use the principles of permutations.

There are 3 distinct positions to be awarded (1st, 2nd, and 3rd) and 12 distinct school teams.
- The 1st position can be won by any of the 12 teams (12 choices).
- The 2nd position can be won by any of the remaining 11 teams (11 choices).
- The 3rd position can be won by any of the remaining 10 teams (10 choices).

Using the fundamental multiplication principle, the total number of ways to award these positions is:
Total ways=12×11×10=1320\text{Total ways} = 12 \times 11 \times 10 = 1320

Alternatively, this can be represented as the number of permutations of 12 distinct objects taken 3 at a time:
12P3=12!(12−3)!=12!9!=12×11×10=1320^{12}P_3 = \frac{12!}{(12-3)!} = \frac{12!}{9!} = 12 \times 11 \times 10 = 1320

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.

Related Comparison Tables

Permutations vs Combinations: The Quantitative Aptitude Guide

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