permutation

(noun)

An ordering of a finite set of distinct elements.

Related Terms

  • factorial
  • multiplicity

Examples of permutation in the following topics:

  • Permutations of Distinguishable Objects

    • The number of permutations of distinct elements can be calculated when not all elements from a given set are used.
    • $ possible permutations, where $n$ represents the number of objects.
    • It is easy enough to use this formula to count the number of possible permutations of a set of distinct objects; for example, the number of permutations of three differently-colored balls.
    • In this case, not all of the cards from the deck are chosen for each possible permutation.
    • Calculate the number of permutations of $n$ objects taken $k$ at a time
  • Permutations

    • A permutation of a set of objects is an arrangement of those objects in a particular order; the number of permutations can be counted.
    • One might define an anagram of a word as a permutation of its letters.
    • The number of permutations of $n$ distinct objects is given by:
    • In mathematics, the notion of permutation is used with several slightly different meanings, all related to the act of permuting (rearranging) objects or values.
    • The study of permutations generally belongs to the field of combinatorics.
  • Permutations of Nondistinguishable Objects

    • Recall that the number of possible permutations of a set of $n$ distinct elements is given by $n!
    • When we encounter multiplicity in a permutation, we must account for it by dividing these possible arrangements out of the total number of permutations that would be possible if all of the elements were distinct.
    • Thus, the number of possible distinct permutations in the set is:
    • Thus, the number of possible distinct permutations can be calculated by:
    • Calculate the number of permutations of a given set of objects, some being nondistinguishable
  • Theoretical Probability

    • Each sequence is called a permutation (or ordering) of the five items.
    • A permutation is an arrangement of unique objects in which order is important.
    • In other words, permutations using all the objects: $n$ objects, arranged into group size of $n$ without repetition, and order being important.
    • The number of possible permutations of a set size of $n$ in which $k$ elements are drawn can be calculated by:
    • By the Fundamental Rule of Counting, the total number of possible sequences of choices is a permutation of each of the items.
  • Combinations

    • A combination is a way of selecting several things out of a larger group, where (unlike permutations) order does not matter.
    • To approach such a question, begin with the permutations: how many possible poker hands are there, if order does matter?
    • Recall the permutation formula: $\displaystyle{\frac{n!}
    • In this case, we can calculate the number of permutations as:
    • is itself a permutation question.
  • Ellipses

    • And of course, the usual rules of permutations apply.
  • Binomial Expansion and Factorial Notation

    • $ also represents the number of possible permutations of $n$, or the number of ways in which $n$ objects can be arranged or selected.
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