Combination with Replacement
Find the number of ways to select items from a set when you can pick the same item multiple times and the order of selection is irrelevant.
What are combinations with replacement?
Combinations with replacement count the number of ways to choose r items from a set of n distinct items where the order doesn't matter and you can pick the same item more than once.
What is the formula for combinations with replacement?
The formula is: C(n + r - 1, r) = (n + r - 1)! / [r! * (n - 1)!]. It is also known as the "stars and bars" formula.
When should I use this instead of standard combinations?
Use this when items can be reused. For example, picking 3 scoops of ice cream from 10 flavors where you can have multiple scoops of the same flavor. Standard combinations assume you pick each flavor at most once.
Can r be greater than n in this calculator?
Yes! Unlike standard combinations, you can choose more items than the total available because you are allowed to repeat items. For example, you can choose 10 items from a set of 2 if repetition is allowed.