Factorial and binomial topics

In mathematics, a multiset (or bag) is a generalization of the concept of a set that, unlike a set, allows multiple instances of the multiset's elements.

In mathematics, and more particularly in number theory, primorial is a function from natural numbers to natural numbers similar to the factorial function, but rather than successively multiplying positive integers, only prime numbers are multiplied.

In mathematics, any of the positive integers that occurs as a coefficient in the binomial theorem is a binomial coefficient.

In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.

In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which yields success with probability p.

In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n.

In mathematics, Pascal's triangle is a triangular array of the binomial coefficients.

In probability theory and statistics, the Poisson distribution (French pronunciation [pwasɔ̃]; in English usually /ˈpwɑːsɒn/), named after French mathematician Siméon Denis Poisson, is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time and/or space if these events occur with a known average rate and independently of the time since the last event.

In probability theory and statistics, the hypergeometric distribution is a discrete probability distribution that describes the probability of successes in draws, without replacement, from a finite population of size that contains exactly successes, wherein each draw is either a success or a failure.

The Sierpinski triangle (also with the original orthography Sierpiński), also called the Sierpinski gasket or the Sierpinski Sieve, is a fractal and attractive fixed set with the overall shape of an equilateral triangle, subdivided recursively into smaller equilateral triangles.

A finite difference is a mathematical expression of the form f(x + b) − f(x + a).

In probability theory and statistics, the gamma distribution is a two-parameter family of continuous probability distributions.

In probability theory and statistics, the beta distribution is a family of continuous probability distributions defined on the interval [0, 1] parametrized by two positive shape parameters, denoted by α and β, that appear as exponents of the random variable and control the shape of the distribution.

In combinatorics, the Eulerian number A(n, m), is the number of permutations of the numbers 1 to n in which exactly m elements are greater than the previous element (permutations with m "ascents").

In mathematics, Mahler's theorem, introduced by Kurt Mahler (), expresses continuous p-adic functions in terms of polynomials.

The binomial approximation is useful for approximately calculating powers of sums of a small number and 1.

In mathematics, a generalized hypergeometric series is a power series in which the ratio of successive coefficients indexed by n is a rational function of n.