What Is a Permutation and Can You Provide an Example?

In summary, a permutation is a rearrangement of a given list or set of objects. It is a 1-1 map of a set onto itself and is not random. Unlike combinations, order does matter in permutations. It can be defined as a number of ordered selections or samplings of objects without repetition.
  • #1
loserone+_+
2
0
what is the permutation?
and like what example?
anyone knows?
 
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  • #2
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.
 
  • #3
i see,
so its just rearrange the list into random right?
 
  • #4
Formally, a permutation is a 1-1 map of a set onto itself.
 
  • #5
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.
 
  • #6
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...
 

FAQ: What Is a Permutation and Can You Provide an Example?

1. What is the meaning of permutation?

Permutation refers to the arrangement of a set of distinct objects in a particular order. It is a mathematical concept used to calculate the number of possible arrangements of a given set of items.

2. How is permutation different from combination?

Permutation takes into account the order of the objects, while combination only considers the selection of objects without regard to their order. For example, 'ABC' and 'CBA' are two different permutations, but the same combination.

3. Can you give an example of a permutation?

One example of a permutation is the arrangement of letters in a word. For instance, the word 'CAT' can be rearranged in six different ways: CAT, ACT, CTA, TAC, ATC, and TCA.

4. How is permutation used in real life?

Permutation has many practical applications, such as in cryptography, genetics, and computer science. It is also used in daily life for tasks like arranging seating arrangements at a wedding or creating unique passwords.

5. What is the formula for calculating permutations?

The formula for calculating permutations is n!/(n-r)!, where n is the total number of objects and r is the number of objects being arranged. '!' represents the factorial operation, which is the product of all numbers from 1 to the given number.

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