binomial coefficient
Choose k formula
A binomial coefficient is a number that appears in the expansion of a binomial expression raised to a power, such as (a + b)ⁿ.
Written as "n choose k" and notated with parentheses or as ⁿCₖ, it tells you how many ways you can select k items from a set of n items without regard to order.
The binomial coefficient for choosing 2 items from 5 is 10.
These numbers form the entries in Pascal's triangle.
Numerical multipliers in expressions
- powersAbilities or authorities held
- termsConditions of an agreement
- exponentiationRaising to a power
- algebraic expressionSymbolic representation of quantities
variables · sequence · index · symmetry · identity · notation · summation · series
Joining of multiple elements
- Pascal's triangleTriangular array of binomial coefficients
- factorialDescending multiplication of integers
- subsetCollection within collection
- selectionChosen item or items
counting · enumeration · partitions · cardinality · unordered · grouping · pairing · arrangements
Favorable outcome attained
- failureLack of success
- outcomeFinal result of events
- expected valueProbability-weighted outcome average
- varianceSpread around the mean
random variable · likelihood · sampling · coin flips · trials
coefficients
Numerical multipliers in expressions
- powersAbilities or authorities held
- termsConditions of an agreement
- exponentiationRaising to a power
algebraic expression · variables · sequence · index · symmetry · identity · notation · summation · series · degree
combination
Joining of multiple elements
- Pascal's triangleTriangular array of binomial coefficients
- factorialDescending multiplication of integers
- subsetCollection within collection
selection · counting · enumeration · partitions · cardinality · unordered · grouping · pairing · arrangements · generating functions
success
Favorable outcome attained
- failureLack of success
- outcomeFinal result of events
- expected valueProbability-weighted outcome average
variance · random variable · likelihood · sampling · coin flips · trials
- Binomial termsscientific name, Latin name, species name
- combinatoricspermutation, combinations, combination, counting, arrangements
- discrete mathcombinatorics, graph theory, set theory, number theory, proofs
- coefficients
- finite differences
- recursionrecursion, base case, self-reference, infinite recursion, recurrence relation