Overview of Permutations and Combinations in JEE Maths

Permutations and Combinations (P&C) form a key part of the Counting Principle in JEE Maths. They help students solve problems related to arrangements, selections, and probability. Understanding P&C is essential for both JEE Main and Advanced exams, as many high-scoring problems are based on these concepts. At StudentBro.in, we provide a comprehensive guide covering formulas, examples, tricks, and practice problems to help students master this topic efficiently.

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What are Permutations and Combinations?

• Permutation: Arrangement of objects in a specific order. Order matters.

• Combination: Selection of objects without considering order. Order does not matter.

Example:

• Permutation: Arrange A, B, C → ABC, ACB, BAC …

• Combination: Choose 2 from A, B, C → AB, AC, BC

Factorials and Basic Counting Principle

• Factorial: n! = n × (n-1) × … × 2 × 1

• Counting Principle: Total ways = Product of choices at each stage

Example: Selecting a 2-digit number from digits 1, 2, 3 → 3 × 2 = 6

Permutations Formula (nPr)

Number of ways to arrange r objects from n objects:

nPr = n! / (n-r)!

Applications:

• Arrangements of letters, digits, or objects in order

• Circular arrangements and repeated objects

Example: Arrange 3 letters from A, B, C, D → 4P3 = 4! / (4-3)! = 24

Combinations Formula (nCr)

Number of ways to select r objects from n objects (order does not matter):

nCr = n! / [r!(n-r)!]

Applications:

• Selection problems in teams or committees

• Choosing objects without regard to order

Example: Select 2 students from 4 → 4C2 = 6

Relationship Between Permutation and Combination

nPr = nCr × r!

This relation is useful for switching between counting arrangements and selections efficiently.

Example: 4P2 = 4C2 × 2! = 6 × 2 = 12

Special Cases in Permutations

1. Repetition allowed: nⁿ arrangements

2. Circular permutation: (n-1)!

3. Permutation with identical objects: n! / (p! q! …)

Example: Arranging letters of "LEVEL" → 5! / (2! 2!) = 30

Special Cases in Combinations

1. Selections with restrictions – Include or exclude certain objects

2. Using symmetry property: nCr = nC(n-r)

3. Multiple groups selection: Use product of combinations

Example: Choose 3 from 5 boys and 2 girls → 5C3 × 2C2 = 10 × 1 = 10

Applications of P&C in JEE Maths

• Arrangement problems: Seats, digits, letters

• Selection problems: Teams, committees

• Probability problems: Favorable outcomes / Total outcomes

• Word formation and repeated letter arrangements

• Circular arrangements for competitive exam problems

Tips and Tricks for JEE Permutations and Combinations

1. Memorize factorial, nPr, nCr formulas

2. Check if order matters → Permutation vs Combination

3. Use symmetry and repetition shortcuts

4. Apply product rule and counting principle in multi-step problems

5. Solve previous year JEE P&C problems for accuracy and speed

Important Formulas to Remember

Permutation Formulas:

• nPr = n! / (n-r)!

• Circular permutation: (n-1)!

• Permutation with repetition: nⁿ

• Permutation of identical objects: n! / (p! q! …)

Combination Formulas:

• nCr = n! / [r!(n-r)!]

• nCr = nC(n-r)

• Multiple group selection: nCk × mCl

StudentBro.in JEE Maths P&C Section

At StudentBro.in, students can access:

• Step-by-step explanations for all P&C problems

• Worked examples for arrangements, selections, circular problems, and repeated objects

• Practice questions with solutions and shortcuts

• Tips for quick problem-solving and exam strategy

• Revision notes for last-minute preparation

Practice Questions and Sample Problems

1. Arrange 3 letters from A, B, C, D → How many ways?

2. Select 2 students from 5 boys and 3 girls → How many ways?

3. Arrange letters of "BALLOON" → Repeated letters

4. Circular arrangement of 6 people → How many ways?

5. Probability problem: 2 students are selected from 5 boys, 3 girls → Probability both are girls

Regular practice improves accuracy, speed, and confidence in solving P&C problems in JEE exams.

Conclusion

Permutations and Combinations are a high-scoring chapter in JEE Maths. Understanding factorials, nPr, nCr, and special cases allows students to solve arrangement, selection, and probability problems quickly and accurately. At StudentBro.in, we provide a complete guide from basics to advanced problem-solving, making P&C simple, practical, and exam-oriented.

Mastering P&C ensures students can tackle counting and probability questions confidently in both JEE Main and Advanced exams.