Permutations and CombinationsMCQMTP Jun 23 - Series IIQuestion 1669 of 251
All Questions

How many numbers of 3 digits can be made by using digits 3, 5, 6, 7 and 8 no. digit being repeated.

Options

A120
B60
C100
DNone of these
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option b — 60

All Options:

  • A120
  • B60
  • C100
  • DNone of these

Ad

Detailed Solution & Explanation

We are given the set of 5 distinct digits: {3,5,6,7,8}\displaystyle \{3, 5, 6, 7, 8\}.
We want to form 3-digit numbers such that no digit is repeated.

To find the total number of such 3-digit numbers, we choose and arrange 3 distinct digits out of the 5 available digits. This is a direct application of permutations:
5P3=5!(5−3)!=5!2!^5P_3 = \frac{5!}{(5-3)!} = \frac{5!}{2!}
Expanding the factorials:
5P3=5×4×3×2×12×1=5×4×3=60^5P_3 = \frac{5 \times 4 \times 3 \times 2 \times 1}{2 \times 1} = 5 \times 4 \times 3 = 60

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

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