Permutations Calculator

Calculate permutations (nPr) and combinations (nCr), including with repetition. View formulas and calculation steps.

The number of ways to arrange r items from n distinct items in order

n (Total items (n))

r (Select items (r))

Permutation

P(n,r) = n! / (n-r)!

Combination

C(n,r) = n! / (r! × (n-r)!)

Permutation with Repetition

n^r (n의 r제곱)

Combination with Repetition

H(n,r) = C(n+r-1, r)

Real-world examples of permutations and combinations.

Permutation Example: Officer Selection

Selecting a president, vice-president, and secretary from 10 people

P(10,3) = 10 × 9 × 8 = 720 ways

Combination Example: Team Formation

Selecting 3 people from 10 to form a team (order doesn't matter)

C(10,3) = 10! / (3! × 7!) = 120 ways