Class 11 Maths Chapter 6 Permutations and Combinations – Revision Notes

Counting problems split into two types depending on whether order matters, and this chapter builds up from the factorial and the fundamental counting principle to the permutation and combination formulas.

Last Updated: September 23, 2026

Fundamental Counting Principle

• m ways × n ways = m×n ways (combined events).

Factorial

• n! = n×(n−1)×…×1; 0! = 1.

Permutations (order matters)

• ⁿP_r = n!/(n−r)!.

Combinations (order doesn’t matter)

• ⁿC_r = n!/[r!(n−r)!].

Relationship

• ⁿP_r = ⁿC_r × r!.

One-Line Summary

Permutations count ordered arrangements while combinations count unordered selections, related by ⁿP_r = ⁿC_r×r!, both built on the factorial and fundamental counting principle.

Frequently Asked Questions

What is the key difference between a permutation and a combination?
A permutation counts arrangements where order matters, while a combination counts selections where order does not matter. Choosing 3 students for a team is a combination, but assigning them captain, vice-captain, and player roles is a permutation.

When should the Fundamental Principle of Counting be used instead of direct formulas for permutations and combinations?
It is used when a problem involves multiple independent stages of selection, and it often forms the reasoning behind deriving the permutation and combination formulas themselves.

Written by Satish

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