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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 items where the order is important, calculated using factorials and a specific formula.
  • Combination
    A selection of items where the order is irrelevant, found by dividing the permutation count by an additional factorial.
  • Factorial
    A product of all positive integers up to a given number, denoted by an exclamation mark.
  • Distinct Objects
    Items that are all different from each other, requiring no adjustment for repeats in counting.
  • Non-distinct Objects
    Items that include repetitions, requiring division by the factorials of repeated counts in arrangements.
  • Outcome
    A possible result from a choice or event, such as a specific outfit or a coin flip result.
  • Arrangement
    A specific order in which items are placed, relevant in permutation problems.
  • Selection
    A group chosen from a larger set, where order may or may not matter depending on context.
  • Notation
    A symbolic representation, such as P(N, R) for permutations or C(N, R) for combinations.
  • Order
    A property indicating whether the sequence of items affects the outcome, crucial for distinguishing permutations from combinations.
  • Team Formation
    A scenario involving the grouping of individuals, typically solved using combinations when order is irrelevant.
  • Lineup
    An ordered sequence of people or items, often addressed with permutation calculations.
  • Appetizer-Entree Pairing
    A practical example of the fundamental counting principle, involving choices from two categories.
  • Word Bank
    A set of possible answers for fill-in-the-blank questions, used in permutation problems when each answer is unique.