What Is a Permutation and Can You Provide an Example?

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    Example Permutation
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Discussion Overview

The discussion centers around the concept of permutations, including definitions and examples. Participants explore the nature of permutations in relation to arrangements of lists and contrast them with combinations.

Discussion Character

  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • One participant asks for a definition and example of a permutation.
  • Another participant defines a permutation as a rearrangement of a list, providing "abc" and its permutations as examples.
  • A participant questions whether permutations are simply random rearrangements.
  • One participant clarifies that permutations are not random but represent all possible arrangements of a set.
  • A further definition is provided, stating that a permutation can be viewed as the number of ordered selections of "K" objects from "N" distinct objects without repetition.

Areas of Agreement / Disagreement

Participants express differing views on whether permutations are random. While some clarify that permutations are systematic arrangements, the initial question about randomness suggests a lack of consensus on this aspect.

Contextual Notes

Some definitions provided may depend on specific interpretations of terms like "ordered" and "distinct," which could lead to varying understandings of permutations.

loserone+_+
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what is the permutation?
and like what example?
anyone knows?
 
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Do you mean "what is a permutation"? A permutation of a given list is simply a rearrangement of the list. For example, if the original list is "abc" then permutations are "acb", "bac", "bca", "cab", "cba", and, for completeness, we include the orignal list, "abc" as a permutation.
 
i see,
so its just rearrange the list into random right?
 
Formally, a permutation is a 1-1 map of a set onto itself.
 
loserone+_+ said:
i see,
so its just rearrange the list into random right?

No, it is NOT random. It is a set of all possible arrangements.

For combinations, on the other hand, order does not matter, so the combinations of abc are abc OR bca OR cab, etc --- but they are all counted as the same thing.
 
we can define permutation as-
1.NUMBER OF ORDERED SELECTION OF "K" OBJECTS OUT OF "N" DISTINCT OBJECTS WITHOUT REPETITION.OR.;
2.ORDERED SAMPLING OF K OBJECTS OUT OF N DISTINCT OBJECTS WITHOUT REPLACEMENT.OR
3.NUMBER OF PERMUTATION(ORDERED SAMPLING)OF K OBJECTS OUT OF N DISTINCT OBJECTS WITHOUT REPETATION...
 

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