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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)
History of combinatorics. The mathematical field of combinatorics was studied to varying degrees in numerous ancient societies. Its study in Europe dates to the work of Leonardo Fibonacci in the 13th century AD, which introduced Arabian and Indian ideas to the continent. It has continued to be studied in the modern era.
The probability is sometimes written to distinguish it from other functions and measure P to avoid having to define "P is a probability" and () is short for ({: ()}), where is the event space, is a random variable that is a function of (i.e., it depends upon ), and is some outcome of interest within the domain specified by (say, a particular ...
First edition. Fat Chance: Probability from 0 to 1 is an introductory undergraduate-level textbook on probability theory, centered on the metaphor of games of chance. [ 1] It was written by Benedict Gross, Joe Harris, and Emily Riehl, based on a course for non-mathematicians taught to Harvard University undergraduates, and published by the ...
The Doctrine of Chances was the first textbook on probability theory, written by 18th-century French mathematician Abraham de Moivre and first published in 1718. [1] De Moivre wrote in English because he resided in England at the time, having fled France to escape the persecution of Huguenots. The book's title came to be synonymous with ...
Combination. In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter (unlike permutations ). For example, given three fruits, say an apple, an orange and a pear, there are three combinations of two that can be drawn from this set: an apple and a pear; an apple ...
In the context of combinatorial mathematics, stars and bars (also called "sticks and stones", [ 1] "balls and bars", [ 2] and "dots and dividers" [ 3]) is a graphical aid for deriving certain combinatorial theorems. It can be used to solve many simple counting problems, such as how many ways there are to put n indistinguishable balls into k ...
Probabilistic number theory. In mathematics, Probabilistic number theory is a subfield of number theory, which explicitly uses probability to answer questions about the integers and integer-valued functions. One basic idea underlying it is that different prime numbers are, in some serious sense, like independent random variables.
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