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Counting definitions

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  • Permutation
    Arrangement of distinct objects where order is important and each object is used only once.
  • Combination
    Grouping of objects where order is irrelevant; only the selection of items matters.
  • Factorial
    Product of all positive integers up to a given number, denoted by an exclamation mark.
  • Fundamental Counting Principle
    Rule stating that the total number of outcomes is the product of the number of choices at each step.
  • Distinct Objects
    Items that are all different from each other, making their arrangement unique.
  • Non-distinct Objects
    Items that are identical, requiring special consideration in counting arrangements.
  • Permutation Formula
    Expression n!/(n−r)! used to calculate arrangements where order matters.
  • Combination Formula
    Expression n!/[r!(n−r)!] used to count groupings where order does not matter.
  • Notation
    Symbols such as P(n, r) or C(n, r) representing permutations or combinations.
  • Numerator
    Top part of a fraction, often representing the total number of arrangements in counting formulas.
  • Denominator
    Bottom part of a fraction, often used to adjust for repeated or unordered selections.
  • Outcome
    A possible result from arranging or selecting objects in a counting problem.
  • Order
    Sequence in which objects are arranged or selected, crucial in distinguishing permutations from combinations.
  • Selection
    Process of choosing objects from a set, regardless of arrangement.
  • Grouping
    Collection of objects considered together, especially when order is not important.