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Permutations and Combinations

NCERT Class 11 Mathematics Chapter 6

Permutations and Combinations for Class 11 Maths and JEE: the counting principle, factorials, nPr and nCr and arrangements with repeated objects.

3 topics Updated 8 Nov 2026

For: Class 11 and JEE

In the syllabus: JEE Class 11 syllabus

With your textbook

NCERT Mathematics (Class 11), Chapter 6 “Permutations and Combinations”, reprint 2026-27.

Open the official NCERT chapter (PDF, 2.4 MB, ncert.nic.in)

Checked on 19 Oct 2026.

Learn in this order

  1. Fundamental principle of counting

    Multiplication and addition principles, filling places with or without repetition, solved examples.

    NCERT Sections 6.1–6.2 9 min read 4 solved examples 8 practice questions

  2. Permutations

    The nPr formula, factorials, repeated letters, vowels together or apart, dictionary order, and solved examples.

    NCERT Section 6.3 14 min read 6 solved examples 11 practice questions

  3. Combinations

    The nCr formula, its link with nPr, its properties and Pascal’s rule, at least and at most selections, solved examples.

    NCERT Section 6.4 12 min read 5 solved examples 11 practice questions

Key formulas in this chapter

Fundamental principle of counting

  • m ways, then n ways: m × n ways
  • m, n, p ways in turn: m × n × p ways
  • n options for each of r places: nr ways

Permutations

  • P = n!/(n − r)!
  • P = n!, P = 1
  • n! = n × (n − 1)! for n ≥ 1; 0! = 1
  • with repetition: n
  • alike objects: n!/(p! p! … p!)

Combinations

  • C = n!/(r! (n − r)!)
  • P = C × r!
  • C = C
  • C + C = C

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