Q1. How many 3-letter words (no repeats) can be formed from A, B, C, D?
Order matters ⇒ permutation ⁴P₃
⁴P₃ = 4!/(4−3)! = 24/1
= 24 words
Permutations and Combinations — Class 11
Order matters for permutations, not for combinations. Compute both instantly and learn when to use which.
Fundamental counting principleIf one event happens in m ways and another in n ways, together they happen in m × n ways.
Factorialn! = n × (n−1) × … × 2 × 1, with 0! = 1.
Permutation (order matters)ⁿPᵣ = n! / (n − r)! — arrangements of r objects from n.
Combination (order doesn't matter)ⁿCᵣ = n! / [r!(n − r)!] — selections of r objects from n.
nPr & nCr calculator Interactive
Enter n and r to get the number of permutations (arrangements) and combinations (selections).
ⁿPᵣ — arrangements—
ⁿCᵣ — selections—
Numericals practice Interactive
Counting problems with steps.
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Solved examples
Formula sheet
| Quantity | Formula |
|---|---|
| Permutations | ⁿPᵣ = n! / (n − r)! |
| Combinations | ⁿCᵣ = n! / [r!(n − r)!] |
| Relation | ⁿPᵣ = r! · ⁿCᵣ |
| Symmetry | ⁿCᵣ = ⁿCₙ₋ᵣ |
Common mistakes & exam wins
- If ORDER matters (arrangements, seating, words) use permutations; if it does not (groups, committees) use combinations.
- Remember 0! = 1 and ⁿCᵣ = ⁿCₙ₋ᵣ.
- ⁿPᵣ = r! × ⁿCᵣ — permutations are just combinations times the arrangements of the chosen items.
Frequently asked questions
What is the difference between a permutation and a combination?
A permutation counts arrangements (order matters); a combination counts selections (order does not matter).
What is the formula for ⁿCᵣ?
ⁿCᵣ = n! / [r!(n − r)!].
What is 0! equal to?
0! is defined to be 1.