permutation

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.