BINOMIAL COEFFICIENT Meaning and
Definition
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A binomial coefficient is a mathematical term used to describe the various coefficients that appear in the expansion of a binomial. In mathematics, a binomial refers to an algebraic expression containing two terms, typically separated by a plus or minus sign. The coefficient of each term represents the numerical factor that multiplies the variable(s) in that term.
The binomial coefficient, often denoted as (n choose k), is a conventional way of representing the number of ways to choose k objects from a set of n distinct objects without considering their order. It corresponds to the number of subsets of size k that can be formed from a larger set of size n.
The binomial coefficient can be computed using a formula known as Pascal's triangle or through other combinatorial methods. It is defined as the product of all positive integers from n down to n - k + 1 divided by the product of all positive integers from 1 up to k. This coefficient plays a crucial role in various areas of mathematics, including probability theory, algebra, and combinatorics.
Binomial coefficients have significant applications in solving problems involving counting, permutations, and combinations. They help determine the possible outcomes and probabilities of various events. In addition, binomial coefficients have connections to polynomial expansions, related series, and even certain properties of algebraic structures.
Common Misspellings for BINOMIAL COEFFICIENT
- vinomial coefficient
- ninomial coefficient
- hinomial coefficient
- ginomial coefficient
- bunomial coefficient
- bjnomial coefficient
- bknomial coefficient
- bonomial coefficient
- b9nomial coefficient
- b8nomial coefficient
- bibomial coefficient
- bimomial coefficient
- bijomial coefficient
- bihomial coefficient
- binimial coefficient
- binkmial coefficient
- binlmial coefficient
- binpmial coefficient
- bin0mial coefficient
- bin9mial coefficient
Etymology of BINOMIAL COEFFICIENT
The term "binomial coefficient" originated from the combination of two words - "binomial" and "coefficient".
- Binomial: The word "binomial" comes from the Latin words "bi-" meaning "two" and "nomen" meaning "name" or "term". It refers to an algebraic expression with two terms or a polynomial with two unlike terms.
- Coefficient: The word "coefficient" finds its roots in the Latin word "coefficiens", which is the present participle of "coefficere". "Co-" means "together" or "with", and "efficere" means "to do" or "to produce". In mathematics, a coefficient is a numerical factor or constant that appears alongside a variable or term.
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