Sentence examples for the binomial coefficient from inspiring English sources

Of these possible outcomes, the number that is favourable to obtaining i red balls and n − i black balls in any one particular order is The number of possible orders in which i red balls and n − i black balls can be drawn from the urn is the binomial coefficient where k! = k × (k − 1) ×⋯× 2 × 1 for positive integers k, and 0! = 1.

where is the binomial coefficient.

where denotes the binomial coefficient.

Note that, which is the binomial coefficient.

/ ( j ! ( k - j ) ! ) is the binomial coefficient.

N w k stands for the binomial coefficient.

The binomial coefficients, or integer coefficients in the expansion of (a + b n, were known to the 12th-century Indian mathematician Bhāskara, who in his Līlāvatī ("The Graceful"), dedicated to a beautiful woman, gave the rules for calculating them together with illustrative examples.

Jia's name was mainly quoted in connection with his method of extracting roots (solutions) of polynomials of degree higher than three and with the related Jia Xian triangle (see the figure), which contains the binomial coefficients for equations up to the sixth degree.

where the binomial coefficients are given by.

where the binomial coefficients are 0 if n

The binomial coefficients are defined by ( λ n ) = λ !