which explains the name " binomial coefficient ".

Carl Linnaeus ( Swedish original name Carl Nilsson Linnæus, 23 May 1707 – 10 January 1778 ), also known after his ennoblement as, was a Swedish botanist, physician, and zoologist, who laid the foundations for the modern scheme of binomial nomenclature.

The same number however occurs in many other mathematical contexts, where it is denoted by ( often read as " n choose k "); notably it occurs as coefficient in the binomial formula, hence its name binomial coefficient.

The cane toad has many other common names, including " giant toad " and " marine toad "; the former refers to its size and the latter to the binomial name, Bufo marinus.

In this case the specific name marinus changes to marina in order to conform with the rules of gender agreement as set out by the International Code of Zoological Nomenclature changing the binomial name from Bufo marinus to Rhinella marina ; the binomial Rhinella marinus was subsequently introduced as a synonym through misspelling by Pramuk, Robertson, Sites, and Noonan ( 2008 ).

He gave it the binomial name Cervus camelopardalis.

The greatest innovation of Linnaeus, and still the most important aspect of this system, is the general use of binomial nomenclature, the combination of a genus name and a second term, which together uniquely identify each species of organism.

The Ostrich was originally described by Linnaeus in his 18th-century work, Systema Naturae under its current binomial name.

He was the first to use both the binomial Ailurus fulgens and the vernacular name " panda " in reference to the species in his description published in 1825 in Histoire Naturelle des Mammifères.

binomial name: Thylacinus cynocephalus, Greek for " dog-headed pouched one " | archivedate = 4 February 2010

# The taxon must be given a name based on the 26 letters in the Latin alphabet ( a binomial for new species, or uninomial for other ranks ).

However, that particular binomial name had been given to the common wombat ( later reclassified as Vombatus ursinus ) by George Shaw in 1800, and was hence unavailable.

In the 10th century, they were given the binomial name of melancholia canina and in the 14th century, daemonium lupum.

Flax ( also known as common flax or linseed ) ( binomial name: Linum usitatissimum ) is a member of the genus Linum in the family Linaceae.

Such a name is called a binomial name ( which may be shortened to just " binomial "), a binomen or a scientific name ; more informally it is also called a Latin name.

We devote a chapter to the binomial distribution not only because it is a mathematical model for an enormous variety of real life phenomena, but also because it has important properties that recur in many other probability models.

When this experiment is viewed as composed of five binomial trials, one for each member of the family, the outcomes of the trials are obviously not independent.

Indeed, the experiment is better viewed as consisting of one binomial trial for the entire family.

that is, we may discuss the phenomenon in terms of its departures from the binomial model.

When each number of successes X is paired with its probability of occurrence Af, the set of pairs Af, is a probability function called a binomial distribution.

The set of all binomial distributions is called the family of binomial distributions, but in general discussions this expression is often shortened to `` the binomial distribution '', or even `` the binomial '' when the context is clear.

The several trials of a binomial experiment produce a new random variable X, the total number of successes, which is just the sum of the random variables associated with the single trials.

Note that t < sup > 0 </ sup > = 1, ( 1 − t )< sup > 0 </ sup > = 1, and that the binomial coefficient,, also expressed as or is:

They are indexed by two nonnegative integers ; the binomial coefficient indexed by n and k is usually written.

It is the coefficient of the x < sup > k </ sup > term in the polynomial expansion of the binomial power ( 1 + x )< sup > n </ sup >.

For any set containing n elements, the number of distinct k-element subsets of it that can be formed ( the k-combinations of its elements ) is given by the binomial coefficient.

The earliest known detailed discussion of binomial coefficients is in a tenth-century commentary, due to Halayudha, on an ancient Hindu classic, Pingala's chandaḥśāstra.

This shows in particular that is a natural number for any natural numbers n and k. There are many other combinatorial interpretations of binomial coefficients ( counting problems for which the answer is given by a binomial coefficient expression ), for instance the number of words formed of n bits ( digits 0 or 1 ) whose sum is k is given by, while the number of ways to write where every a < sub > i </ sub > is a nonnegative integer is given by.

A more general binomial theorem and the so-called " Pascal's triangle " were known in the 10th-century A. D. to Indian mathematician Halayudha and Persian mathematician Al-Karaji, in the 11th century to Persian poet and mathematician Omar Khayyam, and in the 13th century to Chinese mathematician Yang Hui, who all derived similar results .< ref > Al-Karaji also provided a mathematical proof of both the binomial theorem and Pascal's triangle, using mathematical induction.

However, the two parts of a binomial name can each be derived from a number of sources, of which Latin is only one.

In biological taxonomy, a patronym is the second part of a binomial name which is derived from a Latinized surname.

The species ' binomial name is derived from the Latin cuculus ( the cuckoo ) and canorus ( melodious ; from canere, meaning to sing ).

Owing to its supposed fondness for picking up coins, Linnaeus gave it the binomial name Corvus monedula, choosing the specific name mǒnēdŭla, which is derived from moneta, the Latin stem of the word " money ".

The binomial name is derived from Latin Podilymbus, a contraction of podicipes (" feet at the buttocks ", from podici -, " rump -" + pes, " foot ")— the origin of the name of the grebe order — and Ancient Greek kolymbos, " diver ", and podiceps, " rump-headed ", from podici-+ New Latin ceps.

Its binomial names were derived from the Latin strepera, meaning " noisy ", and graculina for resembling a Jackdaw.

However, for most practical pricing models, such as a binomial model, this is not the case and vega must be derived numerically.

The binomial name is derived from the Greek skolopax, meaning ' woodcock ', and Latin rusticus (' rural ') and colere (' to live ').

The form of scientific names for organisms that we know as binomial nomenclature is derived from the noun-adjective form of vernacular names used by prehistoric cultures.

The binomial name is derived from Greek kerthios, a small tree-dwelling bird described by Aristotle and others, and Latin familiaris, familiar or common.

The binomial name is derived from Greek ; kerthios is a small tree-dwelling bird described by Aristotle and others, and brachydactyla comes from brakhus, " short " and dactulos " finger ", which refers, like the English name, to the fact that this species has shorter toes than the Common Treecreeper.

Both parts of the binomial name refer to the aggressive behaviour of the bird at its mating arenas ; Philomachus is derived from Ancient Greek philo-" loving " and machē " battle ", and pugnax from the Latin term for " combative ".

It seems reasonable to assume that the form of scientific names we call binomial nomenclature is derived from this simple and practical way of constructing common names-but with the use of Latin as a universal language.

A binomial name is treated as if it was a Latin phrase in two words, no matter which language the words were originally derived from.

The binomial can be derived as a limiting form, where in such a way that their ratio remains fixed.

The latter half of the Latin binomial dalli is derived from William Healey Dall ( 1845 – 1927 ), an American naturalist.

The binomial name Crocodylus niloticus is derived from the Greek kroko (" pebble "), deilos (" worm ", or " man "), referring to its rough skin ; and niloticus, meaning " from the Nile River ".

Its binomial name is derived from the Mexican town of Campeche, where it is native.

Many series involving the binomial coefficient may be derived:

The binomial name Drosera regia is derived from the Greek word droseros, meaning " dew-covered " and the specific epithet regia comes from the Latin for " royal ", a reference to what Stephens described as its " striking appearance ".