What is "combination"

Combination \Com`bi*na"tion\, n. [LL. combinatio. See Combine.]

1. The act or process of combining or uniting persons and things.

   Making new compounds by new combinations.
   --Boyle.

   A solemn combination shall be made Of our dear souls.
   --Shak.

2. The result of combining or uniting; union of persons or things; esp. a union or alliance of persons or states to effect some purpose; -- usually in a bad sense.

   A combination of the most powerful men in Rome who had conspired my ruin.
   --Melmoth.

3. (Chem.) The act or process of uniting by chemical affinity, by which substances unite with each other in definite proportions by weight to form distinct compounds.

4. pl. (Math.) The different arrangements of a number of objects, as letters, into groups.

   Note: In combinations no regard is paid to the order in which the objects are arranged in each group, while in variations and permutations this order is respected.
   --Brande & C.

   Combination car, a railroad car containing two or more compartments used for different purposes. [U. S.]

   Combination lock, a lock in which the mechanism is controlled by means of a movable dial (sometimes by several dials or rings) inscribed with letters or other characters. The bolt of the lock can not be operated until after the dial has been so turned as to combine the characters in a certain order or succession.

   Combination room, in the University of Cambridge, Eng., a room into which the fellows withdraw after dinner, for wine, dessert, and conversation.

   Combination by volume (Chem.), the act, process, or ratio by which gaseous elements and compounds unite in definite proportions by volume to form distinct compounds.

   Combination by weight (Chem.), the act, process, or ratio, in which substances unite in proportions by weight, relatively fixed and exact, to form distinct compounds. See Law of definite proportions, under Definite.

   Syn: Cabal; alliance; association; league; union; confederacy; coalition; conspiracy. See Cabal.

late 14c., combinacyoun, from Old French combination (14c., Modern French combinaison), from Late Latin combinationem (nominative combinatio) "a joining two by two," noun of action from past participle stem of combinare (see combine (v.)).

n. 1 The act of combining, the state of being combined or the result of combining. 2 An object formed by combining. 3 A sequence of numbers or letters used to open a combination lock. 4 (context mathematics English) One or more elements selected from a set without regard to the order of selection. 5 An association or alliance of people for some common purpose. 6 (context billiards English) A combination shot; a billiard; a shot where the cue ball hits a ball that strikes another ball on the table. 7 motorcycle and sidecar

1. n. 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]

In mathematics, a combination is a way of selecting items from a collection, such that (unlike permutations) the order of selection does not matter. In smaller cases it is possible to count the number of combinations. 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. More formally, a k-combination of a set S is a subset of k distinct elements of S. If the set has n elements, the number of k-combinations is equal to the binomial coefficient

$$\binom nk = \frac{n(n-1)\dotsb(n-k+1)}{k(k-1)\dotsb1}$$
, which can be written using factorials as $\textstyle\frac{n!}{k!(n-k)!}$ whenever k ≤ n, and which is zero when k > n. The set of all k-combinations of a set S is sometimes denoted by $\textstyle\binom Sk\,$.

Combinations refer to the combination of n things taken k at a time without repetition. To refer to combinations in which repetition is allowed, the terms k-selection, k-multiset, or k-combination with repetition are often used. If, in the above example, it was possible to have two of any one kind of fruit there would be 3 more 2-selections: one with two apples, one with two oranges, and one with two pears.

Although the set of three fruits was small enough to write a complete list of combinations, with large sets this becomes impractical. For example, a poker hand can be described as a 5-combination (k = 5) of cards from a 52 card deck (n = 52). The 5 cards of the hand are all distinct, and the order of cards in the hand does not matter. There are 2,598,960 such combinations, and the chance of drawing any one hand at random is 1 / 2,598,960.

In chess, a combination is a sequence of moves, often initiated by a sacrifice, which leaves the opponent few options and results in tangible gain. At most points in a chess game, each player has several reasonable options from which to choose, which makes it difficult to plan ahead except in strategic terms. Combinations, in contrast to the norm, are sufficiently forcing that one can calculate exactly how advantage will be achieved against any defense. Indeed, it is usually necessary to see several moves ahead in exact detail before launching a combination, or else the initial sacrifice would not be undertaken.

A combination is a mathematical collection of things in a context where their specific order is irrelevant.

Combination or combo also may refer to:

• Combination (chess), a relatively long sequence of chess moves
• Combination (jump), in horseback riding
• Combination, parishes in Scotland sharing a poorhouse in the manner of a Poor Law Union
• Group historically called a combination:
  • Trade union
  • Businesses cooperating in price fixing
  • Cabal
• "Combination", song from Rocks (Aerosmith album)
• Combinations (album), by Eisley
• Combinations, underwear of the union-suit style