Calculate nPr (permutations) and nCr (combinations) instantly ā for any n and r values.
The Permutation & Combination Calculator computes both nPr (permutations) and nCr (combinations) simultaneously. These are among the most important concepts in combinatorics and probability, and they appear in virtually every competitive exam in India ā JEE, CAT, GMAT, SSC, IBPS banking exams, and school mathematics.
Permutations (nPr)
A permutation counts arrangements where order matters. nPr = n! / (nār)! tells you how many ways to arrange r items from n distinct items where the order is significant.
Example: How many 3-letter words can be formed from {A, B, C, D}? ā P(4,3) = 4Ć3Ć2 = 24
Combinations (nCr)
A combination counts selections where order doesn't matter. nCr = n! / (r! Ć (nār)!) tells you how many ways to select r items from n distinct items where order is irrelevant.
Example: How many 3-person committees can be formed from 8 people? ā C(8,3) = 56
Key Difference
"AB" and "BA" are the SAME combination but DIFFERENT permutations. If choosing a team (order irrelevant) ā use combination. If assigning roles (president, VP, secretary ā order matters) ā use permutation.
1. Enter n: The total number of items to choose from.
2. Enter r: How many items to choose or arrange.
3. View Results: See both nPr (permutations) and nCr (combinations) simultaneously.
Permutation: nPr = n! / (nār)! = n Ć (nā1) Ć (nā2) Ć ... Ć (nār+1)
Combination: nCr = n! / (r! Ć (nār)!) = nPr / r!
Relationship: nCr = nPr / r! ā combinations are always ā¤ permutations
Special values: nC0 = 1, nC1 = n, nCn = 1, nCr = nC(nār)
Example 1 ā Password: 10 digits, choose 4 for a PIN, order matters: P(10,4) = 5040
Example 2 ā Lottery: Choose 6 from 45 numbers, order doesn't matter: C(45,6) = 8,145,060
Example 3 ā Class Committee: Choose president, VP, secretary from 20 students: P(20,3) = 6,840
Example 4 ā Basketball Team: Choose 5 from 12 players: C(12,5) = 792