AskDefine | Define combination

Dictionary Definition



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
7 the act of combining things to form a new whole [syn: combining, compounding]

User Contributed Dictionary





  1. The act of combining, the state of being combined or the result of combining.
  2. A sequence of numbers or letters used to open a combination lock.
  3. One or more elements selected from a set without regard to the order of selection.
  4. An association or alliance of people for some common purpose.
  5. A combination shot; a billiard; a shot where the cue ball hits a ball that strikes another ball on the table.

Derived terms

Related terms


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
объединение (objedin'énie)
combination shot
  • Finnish: ratsastus

See also

Extensive Definition

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.

See also

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

Synonyms, Antonyms and Related Words

Bund, Rochdale cooperative, accompaniment, accord, accordance, addition, adjunct, admixture, affairs, affiliation, affinity, agglomeration, agglutination, aggregate, aggregation, agreement, alignment, alliance, alloy, alloyage, amalgam, amalgamation, approximation, array, articulation, assemblage, assembly, association, axis, band, blend, blending, bloc, body, bond, bracketing, brew, building, buildup, cabal, cahoots, call-up, canvass, cartel, census, circle, clique, closeness, clustering, co-working, coaction, coadunation, coalescence, coalition, coincidence, collaboration, colleagueship, collection, collectivity, college, collegialism, collegiality, colligation, collocation, colloid, collusion, combine, combined effort, combo, comminglement, commingling, commixture, common market, communication, comparison, composite, composition, compound, comradeship, concatenation, concert, concerted action, concoction, concomitance, concordance, concourse, concurrence, confection, confederacy, confederation, confluence, conflux, confraternity, congeries, conglomerate, conglomeration, congregation, conjugation, conjunction, connectedness, connection, consilience, consolidation, consortium, conspiracy, constitution, construction, consumer cooperative, contiguity, contrariety, convergence, cooperation, cooperative, cooperative society, copartnership, copartnery, copulation, corps, corralling, correspondence, coterie, council, coupling, credit union, customs union, data-gathering, dealings, decoction, decoctum, deduction, disjunction, eclecticism, economic community, embodiment, emulsion, ensemble, fabrication, faction, fashioning, federation, fellowship, filiation, formation, fraternalism, fraternity, fraternization, free trade area, freemasonry, fusion, gang, gathering, getup, group, grouping, homology, hookup, identification, identity, immixture, inclusion, incorporation, individuality, indivisibility, ingathering, intactness, integrality, integration, integrity, intercommunication, intercourse, interfusion, interlarding, interlardment, interlinking, interminglement, intermingling, intermixture, intimacy, inventory, inviolability, irreducibility, joinder, joining, jointure, junction, juxtaposition, knotting, league, liaison, link, linkage, linking, machine, magma, make, makeup, marriage, meeting, melding, mergence, merger, merging, mingling, mix, mixing, mixture, mob, mobilization, mosaic, muster, mutual attraction, nearness, oneness, organic unity, organization, pairing, parasitism, particularity, partnership, party, paste, patchwork, piecing together, pluralism, political machine, pool, propinquity, proximity, purity, putting together, rapport, relatedness, relation, relations, relationship, ring, rodeo, roundup, saprophytism, selfsameness, set, setup, shaping, similarity, simplicity, simultaneity, singleness, singularity, society, sodality, solidarity, solidification, solidity, solution, sorority, splice, structure, structuring, survey, suspension, symbiosis, sympathy, synchronism, syncretism, syndicate, syndication, syneresis, synergy, synthesis, tie, tie-in, tie-up, togetherness, trust, undividedness, unification, uniformity, union, uniqueness, united action, unity, univocity, wholeness, yoking
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