Is there a notion similar to a power set for permuted and ordered elements?

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SUMMARY

The discussion centers on the concept of an "ordered & permuted power set," which considers the arrangement of elements in a set as significant. For a set S containing three singletons {X}, {Y}, and {Z}, the complete collection of subsets includes not only the empty set and individual elements but also all possible permutations of combinations. This results in a total of 15 unique subsets, highlighting the distinction between traditional power sets and this new notion that incorporates order.

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Shaun Culver
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I would like if there is a notion similar to that of a "power set" where the order of the elements in a set is accounted for - the elements are permuted, and each arrangement is considered to be a separate set.

For example:

For three singletons: {X},{Y}, & {Z} in a set S, the "ordered & permuted power set" would consist of the following subsets:

{Empty}
{X}; {Y}; {Z};
{X,Y}; {Y,X}; {X,Z}; {Z,X}; {Y,Z}; {Z,Y}
{X,Y,Z}; {X,Z,Y}; {Y,X,Z}; {Z,X,Y}; {Y,Z,X}; {Z,Y,X}
 
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Please excuse my inexperience - I am new to set theory.
 
Correction: In post #1, after the first three words, "I would like...", please add, "...to know...".
 

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