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Permutation: meaning, definitions and examples

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permutation

 

[pərˈmjuːteɪʃən ]

Definition

Context #1 | Noun

mathematics concept

A permutation is a specific arrangement of a set of objects in a particular order. In mathematics, it refers to the different ways in which a set can be arranged, where the order of arrangement is significant. Permutations are often contrasted with combinations, where the order does not matter. The concept is widely applicable in fields such as statistics, computer science, and cryptography.

Synonyms

arrangement, ordering, sequence.

Examples of usage

  • The permutation of the letters in 'ABC' is 'ABC', 'ACB', 'BAC', 'BCA', 'CAB', 'CBA'.
  • In a race, the different finishing orders of the runners represent permutations.
  • Calculating the number of permutations can help solve complex problems in probability.

Interesting Facts

Mathematics

  • In math, a permutation refers to the different ways of arranging a set of items. For example, there are 6 ways to arrange three items: ABC, ACB, BAC, BCA, CAB, and CBA.
  • Permutations are fundamental in probability, helping calculate the likelihood of different outcomes in any scenario.
  • The formula for finding the number of permutations of n items is n!, which means n factorial (n × (n-1) × (n-2) × ... × 1).

Computer Science

  • Algorithms that generate permutations are essential in computer science, particularly for tasks involving sorting and optimization.
  • In cryptography, permutations are used to create complex encryption methods, ensuring data security.
  • The concept plays a critical role in error-detecting codes, helping to rearrange data for efficient processing.

Biology

  • In genetics, permutations of gene sequences can lead to variations in traits, affecting evolution and species adaptation.
  • The arrangement of amino acids in proteins is a specific permutation that determines the protein’s function in living organisms.
  • Different permutations of DNA sequences can result in distinct genetic expressions, which can influence individual development.

Gaming

  • Many strategy games involve permutations wherein players can take different routes or make varied choices, creating unique game experiences.
  • In card games like Poker, the arrangement of cards is crucial; different permutations lead to different strategies and outcomes.
  • Puzzle games often require players to explore all permutations of pieces to solve challenges efficiently.

Art

  • Artists often explore permutations in their works by rearranging elements to create different visual interpretations.
  • In music, composers use permutations of melodies or harmonies to develop themes and variations within a piece.
  • Dance choreography frequently involves permutations of movements to convey complex stories or emotions.

Word Frequency Rank

With rank #18,873, this word belongs to specialized vocabulary. While not common in everyday speech, it enriches your ability to express complex ideas.