Permutations and CombinationsMTP Sep 24Question 1753 of 159
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A user wants to create a password using $4$ lowercase letters (a-z) and $3$ uppercase letters (A-Z). No letter can be repeated in any form. In how many ways can the password be created if the password must start with an uppercase letter?

Options

A$26 \times 25 \times 24 \times 23 \times 22 \times 5 \times 21$
B$26 \times 25 \times 24 \times 23 \times 22 \times 2 \times 21$
C$26 \times 25 \times 24 \times 23 \times 22 \times 22 \times 21$
D$6 \times 26 \times 25 \times 24 \times 23 \times 22 \times 21$
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Correct Answer

✅ Option a — $26 \times 25 \times 24 \times 23 \times 22 \times 5 \times 21$

All Options:

  • A$26 \times 25 \times 24 \times 23 \times 22 \times 5 \times 21$
  • B$26 \times 25 \times 24 \times 23 \times 22 \times 2 \times 21$
  • C$26 \times 25 \times 24 \times 23 \times 22 \times 22 \times 21$
  • D$6 \times 26 \times 25 \times 24 \times 23 \times 22 \times 21$

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.

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