Formula and example
How it is calculated
Without order or repetition: C(n,k)=n!/[k!(n−k)!]. With order: n!/(n−k)!. With order and repetition: n^k.
Worked example
Ten distinct elements can form 120 groups of three. If order matters, there are 720 arrangements.
Things to check
- Elements are treated as distinguishable. The tool calculates counts, not predictions of winnings.
- Without repetition, k>n gives a count of 0. For k=0, there is exactly one empty selection.
Frequently asked questions
When does order matter?
For a three-digit code, 123 and 321 are different. For a group of the same three people, their listing order usually does not matter.