1 a collection of things that have been combined; an assemblage of separate parts or qualities
2 a coordinated sequence of chess moves
3 a sequence of numbers or letters that opens a combination lock; "he forgot the combination to the safe"
4 a group of people (often temporary) having a common purpose; "they were a winning combination"
5 an alliance of people or corporations or countries for a special purpose (formerly to achieve some antisocial end but now for general political or economic purposes)
6 the act of arranging elements into specified groups without regard to order
- Rhymes: -eɪʃǝn
- The act of combining, the state of being combined or the result of combining.
- A sequence of numbers or letters used to open a combination lock.
- One or more elements selected from a set without regard to the order of selection.
- An association or alliance of people for some common purpose.
- A combination shot; a billiard; a shot where the cue ball hits a ball that strikes another ball on the table.
act of combining
sequence of numbers or letters for a combination lock
- Finnish: yhdistelmä
- German: Kombination
- Russian: комбинация (kombinácija)
- Swedish: kombination
one or more elements selected without regard of the order
- Czech: kombinace
- Finnish: kombinaatio
- German: Kombination
- Russian: комбинация (kombinácija) , сочетание (sočetánije)
- Swedish: kombination
- Finnish: yhdistys
- Finnish: ratsastus
In combinatorial mathematics, a combination is an un-ordered collection of unique sizes. (An ordered collection is called a permutation.) Given S, the set of all possible unique elements, a combination is a subset of the elements of S. The order of the elements in a combination is not important (two lists with the same elements in different orders are considered to be the same combination). Also, the elements cannot be repeated in a combination (every element appears uniquely once); this is often referred to as "without replacement/repetition". This is because combinations are defined by the elements contained in them, thus the set is the same as . For example, from a 52-card deck any 5 cards can form a valid combination (a hand). The order of the cards doesn't matter and there can be no repetition of cards.
A k-combination (or k-subset) is a subset with k elements. The number of k-combinations (each of size k) from a set S with n elements (size n) is the binomial coefficient (also known as the "choose function"):
- C^k_n = = \frac.
where n is the number of objects from which you can choose and k is the number to be chosen, and n! denotes the factorial.
As an example, the number of five-card hands possible from a standard fifty-two card deck is:
- = \frac = \frac = \frac = 2598960.
The number of combinations with repetition can be calculated as:
- = =
For example, if you have ten types of donuts (n) on a menu to choose from and you want three donuts (k) there are (10 + 3 − 1)! / 3!(10 − 1)! = 220 ways to choose (see also multiset).
A combination is a special case of a partition of a set; specifically, a partition into two sets of size k and n − k.
Since it is impractical to calculate n! if the value of n is very large, a more efficient algorithm is
- = \frac \times \frac \times \frac \times \frac \times \cdots \times \frac .
- = \frac \times \frac \times \frac \times \frac \times \frac = 2598960.
You get the same result for n-k as for k. Therefore, when k is more than half of n, it may be easier to compute using n-k in place of k.
- Article on Combinations-PlainMath.Net Example and how to solve a combination
- Many Common types of permutation and combination math problems, with detailed solutions
- The Unknown Formula For combinations when choices can be repeated and order does NOT matter
- Web-based calculator of permutations and combinations
combination in Arabic: التوافيق
combination in Czech: Kombinace
combination in German: Kombinatorik#Kombination_ohne_Zur.C3.BCcklegen
combination in French: Combinaison (mathématiques)
combination in Korean: 조합
combination in Indonesian: Kombinasi
combination in Italian: Combinazione
combination in Latvian: Kombinācija
combination in Hungarian: Kombináció
combination in Dutch: Combinatie (wiskunde)
combination in Japanese: 組合せ (数学)
combination in Polish: Kombinacja bez powtórzeń
combination in Portuguese: Combinação (matemática)
combination in Russian: Сочетание
combination in Albanian: Kombinacioni
combination in Serbian: Комбинација
combination in Finnish: Kombinaatio
combination in Swedish: Kombination (matematik)
combination in Tamil: சேர்வு (கணிதம்)
combination in Thai: การจัดหมู่
combination in Turkish: Kombinasyon
combination in Urdu: تولیف
combination in Chinese: 組合
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