Permutation & Combination Assignment Help

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In mathematics, the notion of permutation is used with several slightly different meanings, all related to the act of permuting (rearranging) objects or values. Informally, a permutation of a set of objects is an arrangement of those objects into a particular order. For example, there are six permutations of the set {1,2,3}, namely (1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), and (3,2,1). One might define an anagram of a word as a permutation of its letters. The study of permutations in this sense generally belongs to the field of combinatorics.

The number of permutations of n distinct objects is n×(n − 1)×(n − 2)×⋯×2×1, which number is called "n factorial" and written "n!".

Generalities :

  • In group theory
  • In combinatorics
  • Permutations in group theory
  • Notation
  • Product and inverse

Permutations in combinatorics :

  • Ascents, descents and runs
  • Inversions
  • Counting sequences without repetition

Permutations in computing :

Numbering permutations

Algorithms to generate permutations

  • Random generation of permutations
  • Generation in lexicographic order
  • Generation with minimal changes

Software implementations

  • Calculator functions
  • Spreadsheet functions

In mathematics a combination is a way of selecting several things out of a larger group, where (unlike permutations) order does not matter. In smaller cases it is possible to count the number of combinations. For example given three fruit, say an apple, orange and pear, there are three combinations of two that can be drawn from this set: an apple and a pear; an apple and an orange; or a pear and an orange. More formally a k-combination of a set S is a subset of k distinct elements of S.

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