Permutations and CombinationsMCQPYQ Jan. 21Question 1611 of 251
All Questions

How many four-digit odd numbers can be formed with digits 0, 1, 2, 3, 4, 7 and 8?

Options

A150
B300
C120
D210
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Correct Answer

✅ Option b — 300

All Options:

  • A150
  • B300
  • C120
  • D210

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Detailed Solution & Explanation

Let us solve this problem assuming that digits cannot be repeated (standard permutation assumption):
The available digits are: {0,1,2,3,4,7,8}\displaystyle \{0, 1, 2, 3, 4, 7, 8\} (total 7 distinct digits).
The odd digits are: {1,3,7}\displaystyle \{1, 3, 7\} (total 3 odd digits).

We want to form a 4-digit odd number:
1. **Unit's place:** To be odd, the unit's place must be occupied by an odd digit. There are 3 choices (from {1,3,7}\displaystyle \{1, 3, 7\}).
2. **Thousand's (first) place:** The first digit cannot be 0 (as it must be a 4-digit number) and cannot be the digit used in the unit's place. Out of 7 digits, 2 are excluded, leaving 7−2=5\displaystyle 7 - 2 = 5 choices.
3. **Hundred's (second) place:** This position can be filled by any of the remaining digits. Since 2 digits have been used, there are 7−2=5\displaystyle 7 - 2 = 5 choices.
4. **Ten's (third) place:** This position can be filled by any of the remaining digits. Since 3 digits have been used, there are 7−3=4\displaystyle 7 - 3 = 4 choices.

By the multiplication principle, the total number of 4-digit odd numbers is:
textTotal=3text(unit′s)times5text(thousand′s)times5text(hundred′s)times4text(ten′s)=300\\text{Total} = 3 \\text{ (unit's)} \\times 5 \\text{ (thousand's)} \\times 5 \\text{ (hundred's)} \\times 4 \\text{ (ten's)} = 300
This matches Option B.
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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