In mathematics a combination is a way of selecting several things out of a larger group, where (unlike permutations) order does not matter. In smaller cases it is possible to count the number of combinations. For example given three fruit, say an apple, orange and 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
which can be written using factorials as whenever, and which is zero when . The set of all k-combinations of a set S is sometimes denoted by .
Combinations can refer to the combination of n things taken k at a time without or with repetitions. In the above example repetitions were not allowed. If however it was possible to have two of any one kind of fruit there would be 3 more combinations: one with two apples, one with two oranges, and one with two pears.
With large sets, it becomes necessary to use more sophisticated mathematics to find the number of combinations. 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.
Other articles related to "combination, combinations":
... The combination artemether/lumefantrine (trade names Coartem and Riamet) is a fixed-dose combination artemisinin-based combination therapy (ACT) indicated for the treatment of acute uncomplicated Plasmodium falciparum ... The combination is an effective and well-tolerated malaria treatment, providing high cure rates even in areas of multi-drug resistance ... In 2001, Coartem became the first fixed dose artemisinin-based combination therapy to meet the World Health Organization's (WHO) pre-qualification criteria for efficacy, safety and ...
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... In the Latter Day Saint movement, a secret combination is a secret society of "people bound together by oaths to carry out the evil purposes of the group." Secret combinations were ... The most notable example of a secret combination is the Gadianton robbers, a conspiracy throughout much of the Book of Mormon narrative ... According to the Joseph Smith Translation of the Bible, Cain also entered a secret combination with Satan and became Master Mahan ...
... become co-specialized, meaning that they are uniquely valuable in combination ... patents and tacit knowledge) of a company provide a synergistic combination of complementary assets ... Such co-specialized assets are therefore more valuable in combination than in isolation ...
... There are various algorithms to pick out a random combination from a given set or list ... One way to select a k-combination efficiently from a population of size n is to iterate across each element of the population, and at each step pick that element with a dynamically changing ...
Famous quotes containing the word combination:
“Hats have never at all been one of the vexing problems of my life, but, indifferent as I am, these render me speechless. I should think a well-taught and tasteful American milliner would go mad in England, and eventually hang herself with bolts of green and scarlet ribbonthe favorite colour combination in Liverpool.”
—Willa Cather (18761947)
“Only amateurs say that they write for their own amusement. Writing is not an amusing occupation. It is a combination of ditch-digging, mountain-climbing, treadmill and childbirth. Writing may be interesting, absorbing, exhilirating, racking, relieving. But amusing? Never!”
—Edna Ferber (18871968)
“The principle of fashion is ... the principle of the kaleidoscope. A new year can only bring us a new combination of the same elements; and about once in so often we go back and begin again.”
—Katharine Fullerton Gerould (18791944)