# Dictionary Definition

combination

### Noun

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

## English

### Pronunciation

/kɒmbɪ'neɪʃən/-
- Rhymes: -eɪʃǝn

### Noun

- 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.

#### Derived terms

#### Related terms

#### Translations

act of combining

- Finnish: yhdistäminen, yhdistely
- German: Kombination
- Russian: соединение (sojedin'énie) , объединение (objedin'énie)
- Swedish: kombination (the state of..), kombinering (the act of...)

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

association

- Finnish: yhdistys

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 .

Example:

- = \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

- Factorial
- Combinadic (how to enumerate combinations and generate i:th combination in a reasonably way)
- Combinatorics
- Multiset
- Permutation
- Probability

## External links

- 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

# 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