MATLAB: Generating matrices of the possible combinations

combinationsmatrix

How do I find all the possible matricies (not their number but the matricies themselves) that are formed as a result of taking a combination of a certain number of columns y from a matrix with a total number of columns x ?
example
X = 1 7 9 10 15
4 8 5 9 21
2 14 3 6 16
here X is 3 by 5 ( 5 columns), now suppose I want to obtain the MATRICIES THEMSELVES that are the result of mixing any of the 3 columns of matrix X
In this case 5c3 , i should obtain 10 matricies, how do I get them ?

Best Answer

X = [1,7,9,10,15;4,8,5,9,21;2,14,3,6,16]
P = nchoosek(1:5,3)
N = size(P,1);
C = cell(1,N);
for k = 1:N
    C{k} = X(:,P(k,:));
end
And checking the output:
>> numel(C)
ans = 10
>> C{:}
ans =
    1    7    9
    4    8    5
    2   14    3
ans =
    1    7   10
    4    8    9
    2   14    6
ans =
    1    7   15
    4    8   21
    2   14   16
ans =
    1    9   10
    4    5    9
    2    3    6
ans =
    1    9   15
    4    5   21
    2    3   16
ans =
    1   10   15
    4    9   21
    2    6   16
ans =
    7    9   10
    8    5    9
   14    3    6
ans =
    7    9   15
    8    5   21
   14    3   16
ans =
    7   10   15
    8    9   21
   14    6   16
ans =
    9   10   15
    5    9   21
    3    6   16
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