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.
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