A tidy sequence of repeated green ivory and brass tiles. Original AI-generated artwork produced for GreenCalc; not a measured diagram or empirical data display.
Identical swaps do not create a new visible sequence
Suppose five tiles contain two green, two ivory and one brass tile, with copies of the same color indistinguishable. Treating all five as distinct gives 5! = 120 arrangements. Each visible color sequence is counted 2! times for the green copies and 2! times for the ivory copies. Dividing gives 5!/(2!2!1!) = 30 distinct sequences.
Enter multiplicities, not a symbol list
In multiset mode, the Permutation Calculator accepts counts such as 2,2,1. It sums them to find the total length and divides the total factorial by each multiplicity factorial. Exact integer arithmetic avoids approximating a potentially large count with a rounded floating-point factorial.
Distinguish indistinguishable copies from repeatable types
A multiset arrangement uses fixed quantities of each type. An ordered string with repetition allows a type to be chosen anew at every position and does not fix its final count. For five positions and three available types, unrestricted repetition gives 3⁵ = 243 strings, which is not the 30 arrangements with the particular multiplicities two, two and one.
List constraints that the basic formula omits
A requirement that the brass tile occupy an endpoint or that matching colors never be adjacent changes the count. So does treating circular rotations as equivalent. The current tool does not silently impose such rules. The roles-versus-committees guide handles the separate order question, while the Password Combination Calculator counts allowed character strings under explicit group requirements rather than fixed multiplicities. Keep the object being counted in the result label so these models are not substituted for one another.
Check the model behind your result
Use the Permutation Calculator for the supported calculation and review its stated assumptions before interpreting the output. Find related tools in the Statistics category, or browse the GreenCalc homepage for other calculation topics.
By GreenCalc Editorial Team · Updated 2026-10-26