Rule of product

The rule of product states that a sequence of choices with fixed numbers of options has as many possible outcomes as the product of those numbers.

Multiplication principle: A counting principle that multiplies the numbers of options at successive stages to count complete outcomes. This is the general counting principle expressed by the rule of product.
Permutations: Ordered arrangements of distinct objects, with order treated as significant. Choosing successive positions without replacement gives the product used to count permutations.
Finite set: A set containing a limited number of elements. The rule applies when each stage draws from a finite number of options.
Rule of sum: A counting principle that adds the numbers of outcomes in mutually exclusive alternatives. It handles alternative cases, whereas the rule of product combines successive choices.
Cartesian product: The set of all ordered tuples formed by choosing one element from each of several sets. Each complete sequence of choices corresponds to one tuple in a Cartesian product.
Passwords: Strings used to authenticate identity, commonly assembled from a defined character set. A fixed character set at each position yields a direct product count of possible strings.
Ordered tuple: A finite sequence of elements in which position determines order. A complete sequence of choices is represented by an ordered tuple.
Inclusion–exclusion principle: A formula for counting a union of sets by correcting for overlaps among them. Overlapping alternatives cannot generally be counted by simply adding their sizes.
Fundamental counting principle: A basic combinatorial rule for counting outcomes formed through multiple successive choices. This is a common name for the rule when choice stages are counted sequentially.
License plate: A vehicle identifier whose letters and numbers follow a jurisdiction's specified format. Each position's allowed symbols can be counted and multiplied to estimate possible plates.

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