# Permutations and Combinations, Class 11 Mathematics | SwaVid Permutations and Combinations, NCERT Class 11 Mathematics: notes with key ideas, formulas, common mistakes and 3 quick checks with worked answers. Canonical: https://www.swavid.com/cbse/class-11/maths/chapter/permutations-and-combinations Source: https://www.swavid.com/cbse/class-11/maths/chapter/permutations-and-combinations # Permutations and Combinations ## Formulas and definitions ## Key ideas ## Common mistakes ## Quick checks ## Keep going ## Questions parents ask ## Class 11 Mathematics on SwaVid ### Fundamental principle of counting ### Factorial notation ### Permutations of distinct objects ### Permutations with repetition and identical objects ### Combinations ### Relation between permutations and combinations ### Next chapter ### Related chapter ### All chapters SwaVid › CBSE › Class 11 › Mathematics › Permutations and Combinations Notes written by SwaVid from the NCERT textbook. Class 11 Mathematics, Chapter 6. Key ideas, formulas and common mistakes. CBSE does not print marks for a single chapter. Short answer. This chapter introduces systematic methods for counting arrangements and selections of objects without listing every possibility. Students learn to use the fundamental principle of counting along with permutation and combination formulas to solve counting problems. Source: NCERT Mathematics (Reprint 2026-27) , Chapter 6, Permutations and Combinations If an event can occur in m different ways, following which a second event can occur in n different ways, then the total number of occurrences of the events in the given order is m × n. This multiplication principle extends to any finite number of successive events. The notation n factorial, written as n!, represents the product of the first n natural numbers for any positive integer n. By standard mathematical convention, 0! is defined to be equal to 1. A permutation is an ordered arrangement of a number of objects taken some or all at a time. The number of permutations of n distinct objects taken r at a time without repetition is denoted by ⁿPᵣ. When repetition of objects is allowed, the number of permutations of n distinct objects taken r at a time is nʳ. The number of permutations of n objects, where p objects are of one kind, q are of another kind, and the rest are distinct, is n! / (p! × q!). A combination is a selection of objects where the order of selection does not matter. The number of combinations of n different objects taken r at a time is denoted by ⁿCᵣ. Each combination of r objects gives rise to r! distinct permutations. Therefore, ⁿPᵣ = ⁿCᵣ × r!, which directly connects selection to ordered arrangement. Try each question first. Then tap it to see the answer. Apply formula ⁿPᵣ = n! / (n - r)! ⁸P₃ = 8! / (8 - 3)! = 8! / 5! 8! / 5! = (8 × 7 × 6 × 5!) / 5! 8 × 7 × 6 = 336 336 Ways to choose 3 boys from 5 boys = ⁵C₃ = 5! / (3! × 2!) = 10 Ways to choose 2 girls from 4 girls = ⁴C₂ = 4! / (2! × 2!) = 6 Total ways by multiplication principle = 10 × 6 = 60 60 Number of available distinct digits n = 5 Number of positions to fill r = 3 Apply formula ⁵P₃ = 5 × 4 × 3 = 60 60 Binomial Theorem . Probability . The 14 chapters of Class 11 Mathematics . The CBSE Class 11 Maths curriculum says it gives no chapter or unit-wise weightage. Theory is 80 marks, plus 20 for internal assessment. No. They are written by SwaVid from the NCERT textbook. The CBSE curriculum is the reference for what is assessed. Binomial Theorem. SwaVid is an AI tutor for Indian students in Classes 6 to 12. It finds the earlier ideas a child missed, then teaches today’s chapter. Start free to see how it works. - Ch 6 NCERT book - 80 marks, theory paper - 3 quick checks - Confusing permutations with combinations . Identify whether the order of elements matters. Use permutations when order determines distinct outcomes, such as forming digits or assigning roles, and use combinations when only group membership matters. - Setting zero factorial equal to zero . Remember that 0! is defined as 1 to keep the factorial formulas consistent for cases like ⁿPₙ and ⁿCₙ. - Adding possibilities instead of multiplying them . Use the multiplication principle when tasks are performed together in succession. Use the addition principle only when two tasks are mutually exclusive alternatives. - Forgetting to divide by factorials for identical letters . When rearranging letters of a word that has repeating characters, divide the total factorial of length n by the factorial of the frequency of each repeating character. ## Key Links - [CBSE](https://www.swavid.com/cbse) - [Class 11](https://www.swavid.com/cbse/class-11) - [Mathematics](https://www.swavid.com/cbse/class-11/maths/chapters) - [Start free →](https://www.swavid.com/signup) - [All 14 chapters](https://www.swavid.com/cbse/class-11/maths/chapters) - [NCERT Mathematics (Reprint 2026-27)](https://ncert.nic.in/textbook.php) - [Open notes](https://www.swavid.com/cbse/class-11/maths/chapter/binomial-theorem) - [Open notes](https://www.swavid.com/cbse/class-11/maths/chapter/probability) - [Class 11 Mathematics](https://www.swavid.com/cbse/class-11/maths/chapters) - [Start free →](https://www.swavid.com/signup)