Last Updated: 6 May 2026Verified for JEE 2027
MathematicsJEE
Difference Between Permutation and Combination
Permutations and combinations are counting techniques. The key difference is that permutations consider order while combinations do not.
Permutation vs Combination — Comparison Table
| Aspect | Permutation | Combination |
|---|---|---|
| Order | Matters | Does not matter |
| Formula | nPr = n!/(n-r)! | nCr = n!/[r!(n-r)!] |
| Meaning | Arrangements | Selections |
| Value | nPr ≥ nCr | nCr ≤ nPr |
| Example | Arranging 3 books on a shelf | Choosing 3 books from 5 |
| Relationship | nPr = nCr × r! | nCr = nPr / r! |
Key Points to Remember
Use permutation when "arrangement" or "order" is mentioned
Use combination when "selection" or "choose" is mentioned
nCr = nC(n-r) — symmetry property
Pascal's Triangle gives combination values
Exam Relevance
This topic falls under Permutations and Combinations in Mathematics for JEE. Questions on the difference between permutation and combination appear frequently in competitive exams, both as direct MCQs and as part of numerical/assertion-reason problems.
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