11. Permutation and Combination - Discrete Mathematics - Vol 2
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11. Permutation and Combination

11. Permutation and Combination

This chapter focuses on permutations and combinations, fundamental concepts in combinatorics. It explores the definitions, formulas, and applications of these concepts, particularly emphasizing the distinctions between ordered and unordered selections. Additionally, the chapter discusses cases where repetitions are allowed and introduces combinatorial proofs to validate the formulas derived.

8 sections

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Sections

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  1. 11
    Permutation And Combination

    This section introduces the concepts of permutations and combinations,...

  2. 11.1
    Introduction To Permutations

    This section introduces permutations, detailing ordered arrangements of...

  3. 11.2
    Definition Of K-Permutation

    This section defines k-permutations and outlines how to calculate the number...

  4. 11.3
    Calculating K-Permutations

    This section discusses the concept of k-permutations, emphasizing how to...

  5. 11.4
    Permutations Where Repetitions Are Allowed

    This section explains the concept of permutations and combinations when...

  6. 11.5
    Combinations And Its Relation To Permutations

    This section explores the concepts of permutations and combinations,...

  7. 11.6
    Unordered Selection Of K Elements

    This section explores unordered selections, known as combinations, focusing...

  8. 11.7
    Combinations With Repetitions

    This section discusses the concept of combinations with repetitions,...

What we have learnt

  • Permutations represent ordered arrangements of objects, with significant distinctions made when the order of selection matters.
  • Combinations refer to unordered selections of objects, where the arrangement is irrelevant.
  • Repetitions can be allowed in selections, affecting the number of possible permutations and combinations.

Key Concepts

-- Permutation
An ordered arrangement of objects where the sequence matters, denoted as P(n, r) for selecting r elements from n.
-- Combination
An unordered selection of objects where the sequence does not matter, denoted as C(n, r) or sometimes as (n choose r).
-- Repetition
The allowance for the same element to be selected multiple times in permutations or combinations.

Additional Learning Materials

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