JEE 2025 Maths | Permutations and Combinations | One Shot Revision | Eduport JEE

Introduction

This tutorial provides a comprehensive guide on Permutations and Combinations, a crucial topic for JEE 2025 Maths preparation. Understanding these concepts will help you solve various combinatorial problems efficiently, which is essential for succeeding in competitive examinations.

Step 1: Understanding Permutations

Permutations refer to the arrangement of items in a specific order. Here’s how to work with permutations:

• Definition: The number of ways to arrange 'n' distinct objects is given by n!.

• Formula:

  • For 'n' objects taken 'r' at a time: [ P(n, r) = \frac{n!}{(n - r)!} ]

• Example:

  • To find the arrangements of 3 letters A, B, C: [ P(3, 3) = 3! = 6 ]
  • Arrangements: ABC, ACB, BAC, BCA, CAB, CBA.

• Practical Tip: Always remember that the order matters in permutations.

Step 2: Understanding Combinations

Combinations are selections of items where order does not matter. Here’s how to deal with combinations:

• Definition: The number of ways to choose 'r' objects from 'n' distinct objects.

• Formula:

  • For 'n' objects taken 'r' at a time: [ C(n, r) = \frac{n!}{r! (n - r)!} ]

• Example:

  • To find the combinations of 3 letters A, B, C taken 2 at a time: [ C(3, 2) = \frac{3!}{2!(3 - 2)!} = 3 ]
  • Combinations: AB, AC, BC.

• Practical Tip: Use combinations when the order is irrelevant, such as forming groups or teams.

Step 3: Applying the Concepts

To effectively apply permutations and combinations:

• Identify the Problem Type: Determine whether the problem requires permutations or combinations based on whether order matters.
• Break Down the Problem: Simplify complex problems into smaller parts.
• Practice with Examples: Solve a variety of problems to strengthen your understanding.

Common Pitfalls to Avoid

• Confusing Permutations with Combinations: Always remember that permutations consider order, while combinations do not.
• Misapplying Formulas: Double-check which formula to use based on the problem's requirements.
• Forgetting Factorials: Ensure you calculate factorials carefully, as they can greatly affect the outcome.

Conclusion

Mastering permutations and combinations is vital for JEE preparation. By understanding the definitions, formulas, and applications, and avoiding common pitfalls, you can tackle combinatorial problems with confidence. Continue practicing a variety of problems to reinforce these concepts and consider downloading the Eduport Learning App for additional resources and practice materials.