Calculate permutations nPr and combinations nCr for set size n and selection r, with or without repetition, plus factorials.
Calculate permutations nPr, combinations nCr, arrangements with repetition, and factorials for any total items n and selection r.
Understanding Permutations and Combinations
Permutations and combinations are counting principles in combinatorics used to determine the total number of possible outcomes when selecting $r$ elements from a set of $n$ elements.
Formulas Overview
Permutations without Repetition (nPr): Order matters, elements cannot repeat. P(n, r) = n! / (n - r)!
Combinations without Repetition (nCr): Order does not matter, elements cannot repeat. C(n, r) = n! / [r! × (n - r)!]
Permutations with Repetition: n^r
Combinations with Repetition: (n + r - 1)! / [r! × (n - 1)!]
How to use
Enter the total number of items n.
Enter the number of items to select r (where r ≤ n).
View nPr, nCr, repetitions, and factorial values instantly.
What is the key difference between permutations and combinations?
Permutations count arrangements where order matters (e.g. lock combinations, race standings). Combinations count selections where order does not matter (e.g. lottery picks, team selections).
What is n factorial (n!)?
n factorial is the product of all positive integers less than or equal to n (e.g., 5! = 5 × 4 × 3 × 2 × 1 = 120).