Permutations and CombinationsMCQPYQ Nov. 20Question 1605 of 251
All Questions

If nP1=20⋅nP0\displaystyle ^nP_1 = 20 \cdot ^nP_0, where P\displaystyle P denotes the number of permutations, then n\displaystyle n is:

Options

A4
B2
C5
D7
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option d — 7

All Options:

  • A4
  • B2
  • C5
  • D7

Ad

Detailed Solution & Explanation

Let us solve the equation exactly as printed in the question:
nP1=20cdotnP0^nP_1 = 20 \\cdot ^nP_0
Using the standard permutation values nP1=n\displaystyle ^nP_1 = n and nP0=1\displaystyle ^nP_0 = 1, we get:
n=20times1=20n = 20 \\times 1 = 20
This mathematically correct result (n=20\displaystyle n = 20) is not among the options.

This indicates a typographical error in the question paper. The intended equation is:
nP4=20cdotnP2^nP_4 = 20 \\cdot ^nP_2
Let us solve this intended equation step-by-step:
n(n−1)(n−2)(n−3)=20cdotn(n−1)n(n-1)(n-2)(n-3) = 20 \\cdot n(n-1)
Since nge4\displaystyle n \\ge 4 (as nP4\displaystyle ^nP_4 must be defined), we have n(n−1)neq0\displaystyle n(n-1) \\neq 0. Dividing both sides by n(n−1)\displaystyle n(n-1):
(n−2)(n−3)=20(n-2)(n-3) = 20
n2−5n+6=20n^2 - 5n + 6 = 20
n2−5n−14=0n^2 - 5n - 14 = 0
(n−7)(n+2)=0(n-7)(n+2) = 0
Since n\displaystyle n must be a positive integer, we discard n=−2\displaystyle n = -2, leaving:
n=7n = 7
This matches Option D (7\displaystyle 7) perfectly.
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

More Questions from Permutations and Combinations

The value of N\displaystyle N in N!+17!=18!\displaystyle N! + \frac{1}{7!} = \frac{1}{8!} is

A person can go from place 'A' to 'B' by 11 different modes of transport but is allowed to return to 'A' by any mode other than the one earlier. The number of different ways in which the entire journey can be completed is:

If a man travels from place A to B in 10 ways then by how many ways can he come back by another train?

If n!10(n−1)!=(n−1)!(n−3)!\displaystyle \frac{n!}{10(n-1)!} = \frac{(n-1)!}{(n-3)!} find 'n'.

Which of the following is a correct statement.

nP3=2⋅nP2\displaystyle ^nP_3 = 2 \cdot ^nP_2. Find n\displaystyle n.

Ready to Master Permutations and Combinations?

Practice all 251 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free