Maths · Class 11 · Permutations and Combinations

Permutations and Combinations for JEE

Everything you need for this topic on one page: the ideas, the formulas, the traps, and free lectures that explain it well.

Last updated: 26 October 2026

Direct answer

Counting principles, arrangements with and without repetition, circular arrangements, selections, distributions and derangements.

Key ideas

Permutations and Combinations: what you must understand

Order matters → permutation; selection only → combination
Identical objects reduce arrangements by the factorial of their count
Circular arrangements of n distinct objects: (n − 1)!
Use complement counting for 'at least one'

Formula sheet

Must-know formulas for Permutations and Combinations

ⁿPᵣ = n!/(n−r)!, ⁿCᵣ = n!/(r!(n−r)!)
Arrangements with repeats: n!/(p!q!…)
Non-negative integer solutions of x₁+…+xᵣ = n: ⁿ⁺ʳ⁻¹Cᵣ₋₁
Derangements Dₙ = n!(1 − 1/1! + 1/2! − … )

One-page formula sheet

Printable Permutations and Combinations formula sheet: formulas, key ideas and traps on one page. Save it as a PDF for offline revision.

Avoid

Common mistakes students make

Double-counting cases
Treating identical objects as distinct
Forgetting necklace arrangements divide by 2

For the exam

How this topic is asked in JEE

Appears frequently. Write cases explicitly. Small cases checked by hand catch most errors.

NCERT map

Where Permutations and Combinations is in NCERT

Chapter names follow the current rationalised NCERT textbooks. Read these sections before solving PYQs.

Class	Book	Chapter	Sections JEE asks from
Class 11	Mathematics	Permutations and Combinations	Fundamental Principle of Counting; Permutations; Permutations when all the objects are not distinct; Combinations

JEE Advanced level

A JEE Advanced-level example on Permutations and Combinations

Question. In how many ways can 8 distinct books be arranged on a shelf such that 3 particular books are never together (meaning no two of these 3 books are adjacent to each other)?

Show solution

Let the 3 restricted books be A, B, C and the remaining 5 books be others. First arrange the 5 other books in 5! = 120 ways.
After placing 5 books, we get 6 gaps (including the two ends): _ B₁ _ B₂ _ B₃ _ B₄ _ B₅ _
To ensure A, B, C are never adjacent, place them in 3 different gaps. Choose 3 gaps from 6 in C(6,3) = 20 ways.
Arrange A, B, C in the chosen 3 gaps in 3! = 6 ways.
Total arrangements = 5! × C(6,3) × 3! = 120 × 20 × 6 = 14400

Answer: 14400

This example was solved twice independently and both solutions agree.

Free lectures

Best free lectures for Permutations and Combinations

Full-chapter free lectures picked from YouTube search results by views, from established JEE channels (mostly in Hinglish). Use the subtopic list to jump straight to the part you need (timestamps come from each video's own chapter list). Watch one, then solve PYQs the same day.

Permutation & Combinations FULL CHAPTER | Class 11th Maths | Arjuna JEE — Arjuna JEE, 5:02:40
Jump to a subtopic (18)
- 00:00 Introduction
- 09:29 Factorial Notation
- 16:08 Fundamental Principle of Counting
- 41:38 Formula For nPr
- 48:26 Theorems of Permutation
- 01:11:01 Permutation of Alike Objects
- 01:35:44 Finding Rank According to Dictionary
- 01:50:30 Circular Permutation (of Distinct Objects)
- 02:10:12 Combinations (Selections)
- 02:23:23 Properties of nCr
- 02:56:48 Formation of Groups
- 03:24:01 Selection of At Least One Object
- 03:50:12 Distribution of Identical Objects (Beggar's Method)
- 04:01:43 Topic : Theorems-Beggar's Method
- 04:04:43 Finding Number of Non Negative Integral Solutions
- 04:25:23 De-Arrangement/Mismatching
- 04:37:18 De-Arrangement - Formula
- 05:01:25 Thank You Bachoo!!
PERMUTATIONS AND COMBINATIONS in One Shot: All Concepts & PYQs Covered | JEE Main & Advanced — JEE Wallah, 7:26:35
Jump to a subtopic (15)
- 00:00 Introduction
- 07:15 Factorial notation
- 18:28 Fundamental principles of counting
- 1:13:55 Theorems of permutations
- 2:29:58 Rank according to dictionary
- 3:29:01 Combinations
- 3:50:03 Diagonal of n-side polygon
- 4:26:56 Formation of groups
- 4:49:14 Exponent of a prime
- 5:03:16 Inclusion -exclusion principle
- 5:33:06 Distribution of identical objects
- 6:17:45 Circular permutations
- 6:27:42 De-arrangement/Mismatch
- 6:38:35 PYQs
- 7:24:04 Thank You Bachhon!

Practise

Where to practise for free

8 JEE Main 2026 PYQs on Permutations and Combinations, with solutions.
Read the chapter in NCERT textbooks (official, free), then solve its NCERT Exemplar (official, free) questions.
Chapter-wise past questions: JEE Main and Advanced PYQs and question bank.
Timed practice tests: NTA Abhyas practice tests (official, free) and our free mock tests.
See it move: interactive simulation.

FAQs

Frequently asked questions

Is Permutations and Combinations important for JEE Main 2027?

Appears frequently. It is part of the official 'Permutations and Combinations' unit in the JEE Main 2027 syllabus.

What are the most important formulas in Permutations and Combinations?

ⁿPᵣ = n!/(n−r)!, ⁿCᵣ = n!/(r!(n−r)!); Arrangements with repeats: n!/(p!q!…); Non-negative integer solutions of x₁+…+xᵣ = n: ⁿ⁺ʳ⁻¹Cᵣ₋₁.

How should I study Permutations and Combinations for JEE?

Understand the key ideas from NCERT or one full lecture, learn the formula sheet, then solve 25–30 past JEE questions on the topic. Write cases explicitly. Small cases checked by hand catch most errors.