JEE Permutations and Combinations Quiz
Practice on arrangements and selections, circular permutations, repeated objects, distribution problems and the counting principles behind them.
Skill map
Levels in this jee permutations and combinations quiz
Every question is generated fresh by AI and calibrated to your level - clear a level and the next one gets harder. Miss one and the AI tutor explains Permutations and Combinations until it sticks, then aims a follow-up at the gap. Want to grind one level? Start the quiz and type that sub-topic as your own.
Exam focus
How Permutations and Combinations is asked
The chapter with the widest gap between how easy the formulas look and how hard the questions are. Very little of the difficulty is computational - it lies in modelling the situation correctly, which is why practice on varied problem types matters more here than in almost any other chapter.
Cheat sheet
Permutations and Combinations formulas worth memorising
| Quantity | Formula |
|---|---|
| Permutations | ⁿPr = n! / (n − r)! |
| Combinations | ⁿCr = n! / (r!(n − r)!) |
| Circular permutations | (n − 1)! |
| Circular, reflections identical | (n − 1)!/2 |
| Arrangements with repeats | n! / (p! q! r! …) |
| Identical items into distinct boxes | ⁿ⁺ʳ⁻¹C(r−1) |
| Selecting any number | 2ⁿ subsets in total |
Marks lost here
Common mistakes in Permutations and Combinations
- Using permutations where order does not matter. Ask whether rearranging the chosen items produces a different outcome - a committee of three is a combination, ranking three positions is a permutation.
- Double counting in circular arrangements. Fixing one position removes the rotational duplicates, which is where (n − 1)! comes from; forgetting this multiplies the answer by n.
- Ignoring repeated identical objects. Arranging the letters of a word with repeated letters requires dividing by the factorial of each repeat count, or the answer is inflated.
- Adding where you should multiply. Use multiplication when stages happen together and addition when cases are mutually exclusive - misreading 'and' versus 'or' is the single most common structural error.
- Solving 'at least one' directly. Counting the complement and subtracting from the total is nearly always faster and much less error-prone.
Game rules
How a round works
- 01Spawn
Press play - the AI generates Permutations and Combinations questions in seconds.
- 02Level up
Answer to earn XP and build a streak. Difficulty adapts to your accuracy and speed.
- 03Learn or lose
Every answer - right or wrong - gets an AI tutor explanation. Wrong answers respawn as follow-ups.
Leaderboard
Permutations and Combinations high scores
Next challenges
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Player's guide
JEE Permutations and Combinations Quiz - FAQs
How do I tell a permutation problem from a combination problem?
Ask whether swapping two selected items changes the outcome. If it does, order matters and you need a permutation; if it does not, use a combination. Words like arrange, rank and seat imply permutations; choose, select and form a group imply combinations.
Why are 'at least' questions easier through the complement?
Because 'at least one' spans many cases, while its complement - none - is a single case. Total minus none gives the answer in one step, whereas adding the cases individually multiplies your chances of missing one.
Is the jee permutations and combinations quiz free?
Yes - completely free, with no sign-up required. Type a topic, press start, and the AI generates an adaptive Permutations and Combinations quiz with an explanation for every answer.
Can teachers host this jee permutations and combinations quiz live for a class?
Yes - create a free teacher account, host a live room on "Permutations and Combinations", and students join with a 6-character code at quff.in/join. No student accounts needed.
From the blog
Permutations and Combinations guides & reading
JEE Permutations and Combinations: 30 Solved Questions
Thirty solved counting questions. The formulas are trivial; modelling the situation correctly is the entire difficulty.
Exam PrepJEE Probability: 30 Practice Questions with Solutions
Thirty solved Probability questions, including the conditional that everyone reverses and the two words that are not synonyms.
More exam prep quizzes
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Six adaptive Permutations and Combinations questions. About two minutes. Climb the podium.