Definition
Permutation
A permutation places chosen objects in a particular order, so position matters.
Continue from this idea into connected AXIO math.
Defining relationship
Same objects, different order, different permutation.
In this elementary sense, a permutation is an ordered arrangement of all or a specified number of distinct objects, with each selected object used once.
permutation 1
permutation 2
A, B, and C are unchanged.
Their order changed, so the permutation changed.
What it means
Imagine lining up objects. Swapping two positions makes a new permutation even though the same objects are present. The question is not only which objects were chosen, but where each one goes.
Remember it
Same objects, different order, different permutation.
Example
Using A, B, and C once each, ABC and BAC are different permutations because A and B changed positions. The six permutations are ABC, ACB, BAC, BCA, CAB, and CBA.
Watch for
Choosing A and B without caring which comes first is an unordered selection, not a permutation in this sense.
Common mix-up
A permutation counts order. An unordered choice does not.
Exact meaning
In this elementary sense, a permutation is an ordered arrangement of all or a specified number of distinct objects, with each selected object used once.