Introduction
The best Unit 7, Permutations and Combinations, solved notes for Class 11 Punjab Boards are now available, with exercises solved using easy, step by step solutions and the marking scheme, based on the new book from PECTAA, the Punjab Curriculum and Textbook Board. These notes are perfect for the 2026 exams and are built to help students score 90 plus marks.
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What’s Inside Unit 7, Counting Without Listing
Unit 7 answers a question that shows up everywhere from exam seating charts to password design: how many ways can something be arranged or chosen, without listing every possibility by hand? The unit builds this up in stages.
It opens with factorial notation, the shorthand n! = n(n − 1)(n − 2)…3·2·1, along with the special case 0! = 1, and shows how factorial expressions simplify and combine.
From there, it moves into permutations, arrangements where order matters, covering the formula nPr = n! / (n − r)!, along with special cases like arrangements with repeated items and circular permutations.
Combinations follow, covering selections where order does not matter, with the formula nCr = n! / [r!(n − r)!], and the relationships between permutations and combinations of the same set.
The unit closes with word problems and applications, translating real situations, forming committees, arranging books on a shelf, choosing a team, into the correct permutation or combination setup.
Exercise 7.1, Factorial Evaluations, Fully Solved
All questions in Exercise 7.1 are fully solved, covering evaluating factorial expressions and simplifying expressions involving n.
| Question | Expression | Result |
|---|---|---|
| Q1(i) | 10! / (0! × 8!) | 90 |
| Q1(ii) | 12! / (3! × 9!) | 220 |
| Q1(iii) | 1440/(3! × 4!) + 2400/(5! × 2!) | 20 |
| Q1(iv) | (n + 2)! / (n + 1)! | n + 2 |
The full solved PDF for Exercise 7.1 is available, covering every question in complete detail.
Exercise 7.2, Permutations, Fully Solved
Exercise 7.2 is fully solved, covering arrangements of distinct objects, arrangements with some items repeated, and circular permutations.
Exercise 7.3, Combinations, Fully Solved
Exercise 7.3 is fully solved, covering selections of objects where order doesn’t matter, and problems that combine both permutations and combinations in the same setup.
Exercise 7.4, Word Problems and Applications, Fully Solved
Exercise 7.4 is fully solved, covering real world word problems built around permutations and combinations, from forming committees and seating arrangements to choosing teams under given restrictions.
Bonus Resources
- A Permutations and Combinations formula sheet PDF for quick reference.
- The top 30 factorial, permutation, and combination shortcuts for faster problem solving.
- Permutations and Combinations video lectures.
- Unit 8, Mathematical Induction and Binomial Theorem, is coming soon as the next unit in this series.
View the Full Solved PDF
The complete solved PDF for Unit 7 is available to view for free.
Why This Unit Matters for Your Overall Score
Permutations and Combinations is a unit where getting the setup right matters more than the arithmetic itself, since choosing between nPr and nCr, or spotting a repeated item or a circular arrangement, decides whether the rest of the solution is even on the right track. Working through Exercise 7.1’s factorial fluency first makes the permutation and combination formulas in Exercises 7.2 and 7.3 far less intimidating, which pays off directly in the word problems of Exercise 7.4.
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Frequently Asked Questions
Which exercises are covered in these Unit 7 notes? Exercise 7.1 through Exercise 7.4 are covered, spanning factorial evaluations, permutations, combinations, and word problem applications.
How do I know whether to use a permutation or a combination? Ask whether order matters. If arranging the items in a different order counts as a different outcome, use a permutation (nPr). If only the group of items chosen matters, regardless of order, use a combination (nCr).
Are past papers included with these notes? Yes, Unit 7 past papers solved from 2018 through 2025 are included as a bonus resource.
Do I need to download the PDF to view these notes? No, the full solved PDF can be viewed directly on the site for free, with no download required.
Conclusion
With Exercise 7.1 through Exercise 7.4 solved, Class 11 students across all nine Punjab boards have a resource for building confidence with Permutations and Combinations ahead of the 2026 exams. Use these notes alongside the bonus formula sheet, shortcuts, and past papers to build both speed and accuracy for your Mathematics exam.
Best of luck for your Class 11 Mathematics exam!