MathLiveBinomial coefficient formula
Gives the number of ways to choose k items from a set of n items without regard to order, for integers 0 ≤ k ≤ n. It is the coefficient of the term x^k y^(n-k) in the expansion of (x+y)^n.
\binom{n}{k} = \frac{n!}{k!\,(n-k)!}What the symbols mean
| total number of items in the set (a non-negative integer) | |
| number of items chosen (an integer with 0 \leq k \leq n) | |
| factorial of n, the product of all positive integers up to n |
About this formula
- FieldMathematics
- TopicCombinatorics
- LevelHigh school
- Also calledn choose k, choose formula, binomial coefficient, combinations formula, number of combinations, nCk
- SourceWikidata Q209875
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