uni/year2/semester1/logseq-stuff/pages/Counting.md

• #MA284 - Discrete Mathematics
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• Next topic: Principle of Inclusion-Exclusion
• Relevant Slides:
• What is Combinatorics? #card card-last-interval:: 97.56 card-repeats:: 5 card-ease-factor:: 2.9 card-next-schedule:: 2023-02-20T09:22:03.466Z card-last-reviewed:: 2022-11-14T20:22:03.466Z card-last-score:: 5
  • Combinatorics is the mathematics of counting.

• The Additive & Multiplicative Principles

  • The Additive Principle

    • What is the Additive Principle? #card card-last-interval:: 75.28 card-repeats:: 5 card-ease-factor:: 2.66 card-next-schedule:: 2023-01-29T02:20:51.719Z card-last-reviewed:: 2022-11-14T20:20:51.720Z card-last-score:: 5
      • If an event A can occur m ways, and event B can occur n (disjoint) ways, then event "A or $B$" can occur m + n ways.

  • The Multiplicative Principle

    id:: 6336be87-7dea-4ba3-b7d0-c77a73bae948
    • What is the Multiplicative Principle? #card card-last-interval:: -1 card-repeats:: 1 card-ease-factor:: 2.56 card-next-schedule:: 2022-11-15T00:00:00.000Z card-last-reviewed:: 2022-11-14T16:42:09.219Z card-last-score:: 1 id:: 6336be87-053a-4ea8-b9cd-9e16b2e801de
      • If event A can occur m ways, and each possibility allows for event B to occur in n (disjoint) ways, then the event "A and $B$" can occur in m \times n ways. id:: 6336be87-2faa-457f-b34f-e11f741673c7

• Counting with Sets

  • What is a set? #card card-last-interval:: 33.64 card-repeats:: 4 card-ease-factor:: 2.9 card-next-schedule:: 2022-12-18T11:06:53.689Z card-last-reviewed:: 2022-11-14T20:06:53.690Z card-last-score:: 5
    • A set is a collection of things.
    • The items in a set are called elements.
    • A set is unordered and does not contain duplicates. i.e.:
      • \{a,b,c\} = \{b,a,c\} = \{a,a, c,b,b,b\}