Binomial coefficient or all combinations
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Syntax
b = nchoosek(n,k)
C = nchoosek(v,k)
Description
example
b = nchoosek(n,k) returns the binomial coefficient, defined as
This is the number of combinations of n items taken k at a time. n and k must be nonnegative integers.
example
C = nchoosek(v,k) returns a matrix containing all possible combinations of the elements of vector v taken k at a time. Matrix C has k columns and m!/((m–k)! k!) rows, where m is length(v).
Examples
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Binomial Coefficient, "5 Choose 4"
Open Live Script
b = nchoosek(5,4)
All Combinations of Five Numbers Taken Four at a Time
Open Live Script
v = 2:2:10;C = nchoosek(v,4)
C = 5×4 2 4 6 8 2 4 6 10 2 4 8 10 2 6 8 10 4 6 8 10All Combinations of Three Unsigned Integers Taken Two at a Time
Open Live Script
v = uint16([10 20 30]);C = nchoosek(v,uint16(2))
C = 3x2 uint16 matrix 10 20 10 30 20 30Input Arguments
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n — Number of possible choices
nonnegative integer scalar
Number of possible choices, specified as a nonnegative integer scalar. n can be any numeric type, but must be real.
Example: 10
Example: int16(10)
Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64
k — Number of selected choices
nonnegative integer scalar
Number of selected choices, specified as a nonnegative integer scalar. k can be any numeric type, but must be real. nchoosek(n,k) requires that n and k be the same type or that at least one of them be of type double.
There are no restrictions on combining inputs of different typesfor nchoosek(v,k).
Example: 3
Example: int16(3)
Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64
v — Set of all choices
vector
Set of all choices, specified as a vector.
Example: [1 2 3 4 5]
Example: [1+1i 2+1i 3+1i 4+1i]
Example: int16([1 2 3 4 5])
Example: [true false true false]
Example: ['abcd']
Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical | char
Complex Number Support: Yes
Output Arguments
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b — Binomial coefficient
nonnegative scalar value
Binomial coefficient, returned as a nonnegative scalar value. b isthe same type as n and k. If n and k areof different types, then b is returned as the nondoubletype.
C — All combinations of v
matrix
All combinations of v, returned as a matrixof the same type as v. Matrix C has k columnsand n!/((n–k)! k!) rows, where n is length(v).
Each row of C contains a combination of k itemschosen from v. The elements in each row of C arelisted in the same order as they appear in v.
If k > numel(v), then C is an empty matrix.
Limitations
When
b = nchoosek(n,k)is sufficientlylarge,nchoosekdisplays a warning that the resultmight not be exact. In this case, the result is only accurate to 15digits for double-precision inputs, or 8 digits for single-precisioninputs.C = nchoosek(v,k)is only practicalfor situations wherelength(v)is less than about15.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
Usage notes and limitations:
When the first input,
x, is a scalar,nchoosekreturns a binomial coefficient. In this case,xmust be a nonnegative integer.When the first input,
x, is a vector,nchoosektreats it as a set.For large single precision outputs, result may not match exactly with MATLAB®.
See Variable-Sizing Restrictions for Code Generation of Toolbox Functions (MATLAB Coder).
Thread-Based Environment
Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.
This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.
Version History
Introduced before R2006a
See Also
perms | combinations
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