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Combinatorics definitions Flashcards

Combinatorics definitions
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  • Fundamental Counting Principle
    A rule stating that the total number of outcomes is found by multiplying the number of choices for each independent event.
  • Permutation
    An arrangement of distinct objects where the order is important, calculated using factorials.
  • Combination
    A selection of objects where the order is irrelevant, using a formula with an extra factorial in the denominator.
  • Factorial
    The product of all positive integers up to a given number, denoted by an exclamation mark.
  • Outcome
    A possible result from a choice or event, such as a specific outfit or roll of a die.
  • Distinct Object
    An item that is unique from others in a set, affecting how arrangements are counted.
  • Non-distinct Object
    An item that is identical to others in a set, requiring adjustment in counting arrangements.
  • Numerator
    The top part of a fraction in counting formulas, often representing the total number of objects factorial.
  • Denominator
    The bottom part of a fraction in counting formulas, often containing factorials to adjust for order or identical items.
  • n
    A variable representing the total number of objects or options in counting problems.
  • r
    A variable representing the number of objects chosen from the total in permutations or combinations.
  • Permutation Notation
    A symbolic way to represent the number of ordered arrangements, often written as P(n, r) or nPr.
  • Combination Notation
    A symbolic way to represent the number of unordered selections, often written as C(n, r) or nCr.
  • Order
    A property indicating whether the sequence of selected objects affects the outcome in arrangements.
  • Arrangement
    A specific sequence or grouping of objects, relevant in both permutations and combinations.