Permutation & Combination Calculator — nPr and nCr
Calculate permutations P(n,r) and combinations C(n,r) with formulas and step-by-step expansion. Includes both ordering and selection formulas.
Examples:
—
P(n,r) — Permutations
—
C(n,r) — Combinations
—
With Repetition (n^r)
—
P/C Ratio (= r!)
Step-by-Step Calculation
Formulas
PermutationP(n,r) = n! / (n-r)!
CombinationC(n,r) = n! / (r! × (n-r)!)
With Repetitionn^r
RelationshipP(n,r) = C(n,r) × r!
Frequently Asked Questions
What is the difference between permutation and combination?
Permutations count arrangements where order matters (selecting a president, VP, and secretary from a group). Combinations count selections where order does not matter (selecting a committee of 3 from a group). For the same n and r: P(n,r) ≥ C(n,r).
What is the formula for permutation?
P(n, r) = n! / (n-r)! — the number of ways to arrange r items from n distinct items. For example, P(5, 2) = 5!/3! = 5 × 4 = 20 (arranging 2 from 5).
What is the formula for combination?
C(n, r) = n! / (r! × (n-r)!) — the number of ways to choose r items from n without regard to order. C(5, 2) = 10. This is also written as "n choose r" or as the binomial coefficient ⁿCᵣ.
What does "n choose r" mean?
"n choose r" (written C(n,r) or ⁿCᵣ) is the number of ways to choose r items from a set of n. It appears in the binomial theorem: (a+b)^n = sum of C(n,k) × a^(n-k) × b^k.
What are permutations with repetition?
If repetition is allowed, the number of ways to arrange r items from n is n^r. For example, a 4-digit PIN from digits 0-9 has 10^4 = 10,000 possibilities (with repetition).