Permutation & Combination Calculator

Calculate permutations (order matters) and combinations (order doesn't matter).

Enter Values

n (total items)

Total number of items to choose from

r (items to choose)

Number of items to select (must be ≤ n)

Permutation vs Combination

Permutation (nPr)

nPr = n! / (n-r)!

Order matters. Example: How many ways can 3 people finish a race (1st, 2nd, 3rd)?

Combination (nCr)

nCr = n! / (r! × (n-r)!)

Order doesn't matter. Example: How many ways can you choose 3 people for a team?

Related Calculators

Calculate standard deviation, variance, and other statistical measures for a dataset.

Determine the required sample size for surveys and statistical studies.

Calculate probabilities for single and multiple events, including conditional probability.

Results

n = 10, r = 3

Permutation (10P3)720

Combination (10C3)120

n!3,628,800

r!6

Formulas Used

10P3 = 10! / (10-3)!

10C3 = 10! / (3! × (10-3)!)