binomial coefficient: meaning, definition, pronunciation and examples
LowTechnical/Formal
Quick answer
What does “binomial coefficient” mean?
A number representing the number of ways to choose a subset of a given size from a larger set, ignoring order.
Audio
Pronunciation
Definition
Meaning and Definition
A number representing the number of ways to choose a subset of a given size from a larger set, ignoring order.
In mathematics, particularly combinatorics, it is the coefficient of the terms in the expansion of a binomial raised to a power (as given by the binomial theorem). It's also a fundamental number in probability, statistics, and various counting problems.
Dialectal Variation
British vs American Usage
Differences
No significant differences in meaning or usage. The notation 'nCk' might be slightly more common in British A-level contexts, while the parentheses notation (n choose k) is universal.
Connotations
Purely mathematical, with no cultural connotations.
Frequency
Equally low frequency in both dialects, confined to technical fields.
Grammar
How to Use “binomial coefficient” in a Sentence
The binomial coefficient [of n and k]The binomial coefficient [for choosing k from n]Vocabulary
Collocations
Examples
Examples of “binomial coefficient” in a Sentence
verb
British English
- N/A
American English
- N/A
adverb
British English
- N/A
American English
- N/A
adjective
British English
- The binomial-coefficient values were listed in a table.
American English
- We used a binomial-coefficient function in the algorithm.
Usage
Meaning in Context
Business
Virtually never used.
Academic
Core terminology in mathematics, statistics, computer science, and engineering courses.
Everyday
Extremely rare outside of specific educational or professional settings.
Technical
Essential in combinatorics, probability theory, algebra, and algorithm analysis.
Vocabulary
Synonyms of “binomial coefficient”
Strong
Neutral
Weak
Vocabulary
Antonyms of “binomial coefficient”
Watch out
Common Mistakes When Using “binomial coefficient”
- Pronouncing 'binomial' as 'bee-nominal'.
- Confusing it with 'binomial distribution' (which uses binomial coefficients but is a different concept).
- Using it as a verb (e.g., 'I binomial coefficiented the numbers' is wrong).
FAQ
Frequently Asked Questions
Yes, essentially. The binomial coefficient C(n, k) gives the number of combinations (i.e., subsets) of size k from a set of n distinct elements.
It is read aloud as "n choose k," which directly describes its function.
In lottery probability calculations (choosing numbers), in genetics (combinations of genes), in quality control (sampling defective items), and in computer science (algorithm complexity).
The entries in Pascal's Triangle are precisely the binomial coefficients. The nth row contains the coefficients for the expansion of (x + y)^n.
A number representing the number of ways to choose a subset of a given size from a larger set, ignoring order.
Binomial coefficient is usually technical/formal in register.
Phrases
Idioms & Phrases
- “N/A”
Learning
Memory Aids
Mnemonic
Think: Bi-NO-mial Coefficient = Number Of ways to choose. The 'bi' can remind you of 'two' (like in binomial, two terms), and coefficient is the number in front.
Conceptual Metaphor
A 'choice counter' or a 'combination counter'.
Practice
Quiz
What does the binomial coefficient C(7, 2) represent?