Permutations & Combinations for JEE Maths
Permutations & Combinations (P&C) is one of the trickiest topics in JEE Maths — not because the formulas are hard, but because the problems require careful logical thinking. A single miscount can give the wrong answer. The good news: with the right approach, P&C problems become systematic.
Prerequisites: Basic counting and factorial notation
What JEE Tests in P&C
Common JEE problem types:
- Arranging objects with/without repetition
- Selecting objects from groups (combinations)
- Circular permutations (seating arrangements)
- Distribution problems (distributing identical/distinct objects into groups)
- Derangements (no object in its original position)
- Problems with restrictions (specific items must/must not be together)
- Binomial theorem (closely linked — nCr appears as binomial coefficients)
The Fundamental Counting Principle
Before memorizing formulas, internalize this: if task A can be done in m ways and task B in n ways, then A followed by B can be done in m × n ways (multiplication principle), and A or B can be done in m + n ways (addition principle).
Every P&C problem ultimately reduces to these two principles. The skill is in breaking the problem into independent tasks.
nPr = n!/(n-r)! counts arrangements (order matters). nCr = n!/(r!(n-r)!) counts selections (order doesn't matter). The relationship: nPr = nCr × r!.
JEE Problem-Solving Framework
Step 1: Determine if the problem is about arrangement (permutation) or selection (combination). Ask: does order matter?
Step 2: Check for restrictions. If certain items must be together, treat them as a single unit. If certain items must NOT be together, use complementary counting: Total - Unfavorable.
Step 3: For distribution problems, identify if objects are identical or distinct, and if groups are distinguishable or not. This determines the formula.
Step 4: For 'at least' problems, use complementary counting: P(at least 1) = Total - P(none).
Step 5: Always verify with a small example. If the formula gives 10 ways for a simple case, list them out to check.
Key Formulas
Common Mistakes to Avoid
- Mistake: Confusing permutation and combination (does order matter in this problem?)
- Mistake: Double counting in problems with identical objects
- Mistake: Forgetting to divide by r! when selecting identical groups
- Mistake: Not considering circular vs linear arrangement
- Mistake: Using nPr instead of nCr in binomial coefficient problems
How to Practice This Topic
P&C requires careful, slow practice — not speed. Do 5 problems per day, writing out the logic for each step. Start with basic counting, move to restrictions, then distribution problems. Review mistakes thoroughly — a wrong P&C approach teaches more than a correct one.
Formula Sheets
Practice Permutations & Combinations Now
Solve questions with step-by-step explanations on TimeBack
Start Free Practice