What is combinations with replacement?

Choosing r items from n types when you can pick the same type more than once. Order does not matter.

C(n+r-1, r) = (n+r-1)! / (r! × (n-1)!). Same as 'stars and bars'.

Yes. All tools on QuickFreeTools are free with no signup.

Online Combinations with Replacement Calculator

Calculate the number of ways to choose r items from n with repetition allowed. Formula: C(n+r-1, r).

n (types)

r (choose)

What is combinations with replacement?: Choosing r items from n types when you can pick the same type more than once. Order does not matter.
What is the formula?: C(n+r-1, r) = (n+r-1)! / (r! × (n-1)!). Same as 'stars and bars'.
Is this tool free?: Yes. All tools on QuickFreeTools are free with no signup.

Celsius to Fahrenheit Converter

Convert Celsius to Fahrenheit and Fahrenheit to Celsius instantly. Free temperature converter.

Tip Calculator

Calculate tip and split the bill. Enter bill amount, tip percentage, and number of people.

Roman Numeral Converter

Convert numbers to Roman numerals and Roman numerals to numbers. Supports 1–3999.

Combinations Calculator

Calculate C(n,r) — the number of ways to choose r items from n without order. Uses n!/(r!(n-r)!).

Even Permutations Calculator

Count how many permutations of n objects are even (expressible as an even number of swaps). For n ≥ 2, equals n!/2.

Factorial Calculator

Calculate n! (n factorial) — the product of all positive integers from 1 to n.