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Counting definitions

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  • Permutation
    Ordered arrangement of distinct objects, where each item occurs only once and order is important.
  • Combination
    Unordered selection of objects, where the order does not affect the outcome and each group is unique.
  • Factorial
    Product of all positive integers up to a given number, used to calculate arrangements and selections.
  • Fundamental Counting Principle
    Method for finding total outcomes by multiplying the number of choices for each event.
  • Distinct Objects
    Items that are different from each other, so each arrangement is unique.
  • Non-distinct Objects
    Items that are identical, requiring adjustment in counting to avoid duplicate arrangements.
  • Permutation Formula
    Equation using n factorial divided by (n minus r) factorial to count ordered arrangements.
  • Combination Formula
    Equation using n factorial divided by (n minus r) factorial times r factorial to count unordered groups.
  • Notation
    Symbols like P(n, r) or C(n, r) used to represent permutations and combinations in problems.
  • Outcome
    Possible result of an arrangement or selection, influenced by whether order matters.
  • Word Bank
    Set of available options for selection, often used in fill-in-the-blank problems.
  • Team Formation
    Grouping of individuals from a larger set, where order may or may not matter.
  • Arrangement
    Specific ordering of objects, relevant in permutation problems.
  • Selection
    Choosing items from a set, relevant in combination problems.
  • Canceling Factorials
    Simplifying calculations by rewriting numerators and denominators to eliminate common factorial terms.