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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 and an orange; or a pear and an orange.
It can be used to solve many simple counting problems, such as how many ways there are to put n indistinguishable balls into k distinguishable bins. [4] The solution to this particular problem is given by the binomial coefficient ( n + k − 1 k − 1 ) {\displaystyle {\tbinom {n+k-1}{k-1}}} , which is the number of subsets of size k − 1 that ...
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures.It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science.
These Calculators Make Quick Work of Standard Math, Accounting Problems, and Complex Equations Stephen Slaybaugh, Danny Perez, Alex Rennie May 21, 2024 at 2:44 PM
The McNuggets version of the coin problem was introduced by Henri Picciotto, who placed it as a puzzle in Games Magazine in 1987, [19] and included it in his algebra textbook co-authored with Anita Wah. [20] Picciotto thought of the application in the 1980s while dining with his son at McDonald's, working out the problem on a napkin.
Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
In this case the problem reduces to n − 2 people and n − 2 hats, because P 1 received h i ' s hat and P i received h 1 's hat, effectively putting both out of further consideration. For each of the n − 1 hats that P 1 may receive, the number of ways that P 2, ..., P n may all receive hats is the sum of the counts for the two cases.
Combinatorial explosion is sometimes used to justify the intractability of certain problems. [ 1 ] [ 2 ] Examples of such problems include certain mathematical functions , the analysis of some puzzles and games, and some pathological examples which can be modelled as the Ackermann function .
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