nchoosek (MATLAB Function Reference)

Binomial coefficient or all combinations

C = nchoosek(n,k)
C = nchoosek(v,k)

Description

C = nchoosek(n,k)

where n and k are nonnegative integers, returns
n!/((n-k)! k!). This is the number of combinations of n things taken k at a time.

C = nchoosek(v,k),

where v is a row vector of length n, creates a matrix whose rows consist of all possible combinations of the n elements of v taken k at a time. Matrix C contains n!/((n-k)! k!) rows and k columns.

Examples

The command nchoosek(2:2:10,4) returns the even numbers from two to ten, taken four at a time:

     2     4     6     8
     2     4     6    10
     2     4     8    10
     2     6     8    10
     4     6     8    10

Limitations

This function is only practical for situations where n is less than about 15.