Permutations and CombinationsMCQMTP May 19Question 1639 of 251
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If nPr=720\displaystyle ^nP_r = 720 and nCr=120\displaystyle ^nC_r = 120 then value of r\displaystyle r is

Options

A4
B5
C3
D6
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Correct Answer

✅ Option c — 3

All Options:

  • A4
  • B5
  • C3
  • D6

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Detailed Solution & Explanation

Let us solve the problem using the fundamental relationship between permutations and combinations:
nPr=r!timesnCr^nP_r = r! \\times ^nC_r
We are given:
- nPr=720\displaystyle ^nP_r = 720
- nCr=120\displaystyle ^nC_r = 120

Substitute these values into the formula:
720=r!times120720 = r! \\times 120
r!=frac720120r! = \\frac{720}{120}
r!=6r! = 6
Since 3!=3times2times1=6\displaystyle 3! = 3 \\times 2 \\times 1 = 6, we have:
r=3r = 3
This matches Option C.
Hence, **Option C** 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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