What is the difference between permutation and combination?

Order creates different outcomes in a permutation. A combination considers only the selected group and ignores order.

How do I calculate a permutation?

An ordered selection of r items from n is P(n,r)=n!/(n−r)!

How do I calculate a combination?

An unordered selection of r items from n is C(n,r)=n!/(r!(n−r)!).

What is the permutation with repetition formula?

For r positions with n choices each, where choices may be reused, the result is n to the power r.

What is the combination with repetition formula?

An unordered selection of r reusable items from n types is C(n+r−1,r).

Why is 0 factorial equal to 1?

There is one way to arrange an empty set. Defining 0! as 1 also keeps factorial identities consistent.

Is a binomial coefficient the same as a combination?

Yes. The binomial coefficient n choose r equals C(n,r).

Does the calculator round large results?

No. It uses BigInt integer arithmetic and displays exact results throughout the supported input range.

Tools/🧮 Calculators/Permutation & Combination Calculator

Permutation & Combination Calculator

Calculate permutations, combinations, selections with repetition, factorials, and binomial coefficients exactly.

Version 1.0 · Last Updated: August 10, 2026 · Maintained by ToolLarder

Permutation, combination, and factorial calculations

Solve selection problems where order matters or does not matter with the appropriate formula. Large results are calculated as exact integers without rounding.

Permutation calculator (nPr)

Find the number of ways to select and arrange r items from n distinct items when order matters.

P(n,r) = n! / (n−r)!

Permutation with repetition

When each of r positions can independently use any of n choices, including repeated choices, there are n to the power r arrangements.

nʳ

Combination calculator (nCr)

Find the number of ways to choose r items from n distinct items when order does not matter.

C(n,r) = n! / (r!(n−r)!)

Combination with repetition

Count unordered selections of r items from n types when a type may be selected more than once.

C(n+r−1,r)

Factorial calculator

n factorial is the product of positive integers from 1 through n; 0 factorial is defined as 1.

n! = n×(n−1)×…×1

Binomial coefficient calculator

A coefficient in a binomial expansion equals the number of ways to choose r items from n.

(n choose r) = C(n,r)