Define a complete choice
Try a useful case
What do these rules mean?
The available labels are distinct types, named A–H. When reuse is allowed, each type has an unlimited supply. When reuse is forbidden, each type can appear at most once.
With order ignored, a sorted list is a multiset: repeated labels still count. AAB and ABA describe the same multiset; AAB and ABB do not.
This lab counts fixed-size choices. It does not model circular arrangements, finite inventories with several copies, or additional restrictions.
Ready to count.
| Outcome model | Reuse allowed | No reuse |
|---|---|---|
| Order matters | ||
| Order ignored |
The file includes the applied rules, exact count and every row on this page. Other pages are not included.
Read the count before reaching for a formula
- Ordered, reuse: each of the k positions has n choices, so multiply n by itself k times.
- Ordered, no reuse: each position removes one available label.
- Unordered, no reuse: every group of k distinct labels has k! orders, so divide the ordered count by k!.
- Unordered, reuse: count how many of each type are selected. Item marks separated into n groups give C(n + k − 1, k), for n > 0.
Selecting zero items always gives one empty outcome. With no available labels, selecting a positive number of items is impossible.