Combinations with replacement allow for selecting items from a set where the same item can be chosen more than once. The formula for combinations with replacement is:
CR(n, r) = (n + r - 1) C r = (n + r - 1)! / (r! * (n - 1)!)
Welcome to our Combination with Replacement Calculator, a simple and efficient tool to help you calculate the number of ways you can select items from a larger set when repetition is allowed and order does not matter.
Combinations with replacement allow for selecting items from a larger set where:
In other words, you are selecting items with the possibility of repeating them, but the order of selection does not change the result. For example, if you're selecting 3 fruit types from a basket containing 4 fruits (Apple, Banana, Cherry, and Grape), you could choose Apple more than once (e.g., Apple, Apple, Banana) or any other combination.
The formula for calculating combinations with replacement is:
C(n + r - 1, r) = (n + r - 1)! / (r!(n - 1)!)
Where:
Let’s say you want to choose 3 items from a set of 5 different colored balls (Red, Blue, Green, Yellow, and Purple), and repetition is allowed. The number of possible combinations can be calculated as follows:
C(5 + 3 - 1, 3) = 7! / (3! * 4!) = 35
So, there are 35 possible combinations of selecting 3 balls from a set of 5 with repetition.
Enter your values in the input fields and click "Calculate" to find the number of possible combinations with repetition. Our Combinations with Replacement Calculator is fast, free, and easy to use.