Maths · Class 11 · Chapter 6
Permutations and Combinations
11 lessons 90 min 2 simulations
This chapter counts without listing. It starts from the multiplication principle and counting in cases, introduces factorials, and builds the formulas for permutations (arrangements, where order matters), including arrangements with conditions and with repeated objects. It then covers combinations (selections, where order does not matter), their properties and Pascal's rule, selections with conditions, problems that select and then arrange, and dictionary order.
What the exam asks
Permutations and combinations are a regular JEE Main topic, and the same counting feeds probability and the binomial theorem. Questions test choosing between nPr and nCr, handling a zero that cannot lead, keeping objects together or apart, dividing for repeated letters, 'at least' selections by cases or by subtraction, and the rank of a word in dictionary order. Most lost marks come from counting ordered and unordered cases the same way.
Lessons
11 lessons · 90 min
1The multiplication principleNCERT §6.1, §6.27 min2Counting in casesNCERT §6.27 min3Factorial notationNCERT §6.3.27 min4Permutations of distinct objectsNCERT §6.3, §6.3.1, §6.3.311 min 1 sim5Arrangements with conditionsNCERT §6.3.37 min6Permutations with repeated objectsNCERT §6.3.46 min7CombinationsNCERT §6.46 min8Properties of combinationsNCERT §6.410 min 1 sim9Selection with conditionsNCERT §6.47 min10Selecting then arranging, and dictionary orderNCERT §6.47 min11Chapter reviewMust-know facts, traps and formulas15 min