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The birthday problem has been generalized to consider an arbitrary number of types. [20] In the simplest extension there are two types of people, say m men and n women, and the problem becomes characterizing the probability of a shared birthday between at least one man and one woman. (Shared birthdays between two men or two women do not count.)
The name is based on the birthday paradox. Choose m birthdays in a year of n days. List the spacings between the birthdays. If j is the number of values that occur more than once in that list, then j is asymptotically Poisson-distributed with mean m 3 / (4n).
More generally, there are d! possible orders for a given array, one for each permutation of dimensions (with row-major and column-order just 2 special cases), although the lists of stride values are not necessarily permutations of each other, e.g., in the 2-by-3 example above, the strides are (3,1) for row-major and (1,2) for column-major.
A logical spreadsheet is a spreadsheet in which formulas take the form of logical constraints rather than function definitions.. In traditional spreadsheet systems, such as Excel, cells are partitioned into "directly specified" cells and "computed" cells and the formulas used to specify the values of computed cells are "functional", i.e. for every combination of values of the directly ...
Combinations and permutations in the mathematical sense are described in several articles. Described together, in-depth: Twelvefold way; Explained separately in a more accessible way: Combination; Permutation; For meanings outside of mathematics, please see both words’ disambiguation pages: Combination (disambiguation) Permutation ...
The usual way to prove that there are n! different permutations of n objects is to observe that the first object can be chosen in n different ways, the next object in n − 1 different ways (because choosing the same number as the first is forbidden), the next in n − 2 different ways (because there are now 2 forbidden values), and so forth.
The (n−1)! different permutations so produced precisely exhaust the set of cycles of length n: each such cycle has a unique cycle notation with the value n in the final position, which allows for (n−1)! permutations of the remaining values to fill the other positions of the cycle notation.
In computer science and mathematics, the Josephus problem (or Josephus permutation) is a theoretical problem related to a certain counting-out game. Such games are used to pick out a person from a group, e.g. eeny, meeny, miny, moe. A drawing for the Josephus problem sequence for 500 people and skipping value of 6.