Introduction to Permutation and Combination for JEE Main

The chapter Permutation and Combination is a fundamental topic in Class 11 Maths, forming the backbone for probability, counting problems, and algebraic reasoning in JEE Main.

• Permutation: Arrangement of objects in a specific order.

• Combination: Selection of objects without considering order.

Understanding formulae, methods, and logical reasoning is crucial for solving JEE Main numerical and MCQs.

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Factorial Notation

• Denoted by n! (n factorial)

• n! = n × (n – 1) × (n – 2) × … × 3 × 2 × 1

• 0! = 1

• Used in permutations, combinations, and probability calculations

Permutation

1. Definition:
Permutation is an arrangement of objects in a specific order.

2. Formula:

• nPr = n! / (n – r)!, where n = total objects, r = objects selected

3. Special Cases:

• Permutations with repetition: n^r

• Permutations with identical objects: n! / (p! q! r! …)

4. Applications:

• Arranging letters, numbers, or people in order

• Circular permutations (arranging objects in a circle)

Example:

• Number of ways to arrange letters in “JEE” → 3! / 2! = 3

Combination

1. Definition:
Combination is a selection of objects where order does not matter.

2. Formula:

• nCr = n! / [r!(n – r)!]

3. Properties:

• nCr = nC(n – r)

• Σ nCr = 2^n (sum of all combinations)

4. Applications:

• Selecting teams, committees, or groups

• Choosing items from a collection

Example:

• Number of ways to choose 2 students from 5 → 5C2 = 10

Fundamental Counting Principle

• If an event can occur in m ways and a second event in n ways, then both events occur in m × n ways

• Extended to multiple events: multiply the number of choices for each step

• Basis for many permutation and combination problems in JEE Main

Advanced Problems in Permutation and Combination

1. Repetition Allowed – when objects can be repeated in selection

2. Restriction Problems – when certain positions or items are restricted

3. Circular Arrangement – arranging objects in a circle

   • Number of arrangements = (n – 1)!

4. At least / At most Problems – combine multiple cases

Relationship Between Permutation and Combination

• nPr = nCr × r!

• Combination is derived from permutation by removing the effect of order

• Useful for converting complex problems into simpler steps

Applications of Permutation and Combination in JEE Main

• Counting arrangements and selections in algebra problems

• Basis for probability problems

• Solving real-life arrangement or selection questions

• Frequently tested in numerical, integer-type, and MCQs

Important JEE Main Preparation Tips for Permutation and Combination

• Memorize factorial, nPr, nCr formulas, and properties

• Practice problems with repetition, restrictions, and circular arrangements

• Use fundamental counting principle for multi-step problems

• Solve previous year JEE Main MCQs and numerical problems

• Focus on relationship between permutation and combination for faster solutions

Why Study Permutation and Combination from Studentbro.in?

Studentbro.in provides:

• Step-by-step explanations of permutation and combination problems

• Solved examples for arrangement, selection, and counting problems

• Charts and formula tables for quick revision

• MCQs and PYQs aligned with JEE Main syllabus

Conclusion

The Permutation and Combination chapter is fundamental and scoring in Class 11 Maths for JEE Main. Mastery of factorials, nPr, nCr, counting principle, and advanced arrangement problems helps students solve both conceptual and numerical problems efficiently.

Studentbro.in provides structured, easy-to-understand, and exam-focused content to master Permutation and Combination effectively and boost JEE Main scores.