Statistical method to arrange a set of variables in subsets

dear all

i have a general mathematical question

i have an array of different numbers. size of the array is 16 x 6. i want to form a subset of a vector of size 1 x6 . each element of the vector is selected from the column that have the same index as this element .

example:

master Array is =
a1 b1 c1 d1 e1 f1
a2 b2 c2 d2 e2 f2
a3 b3 c3 d3 e3 f3
.
.
.
a16 b16 c16 d16 e16 f16

subset = a1 b2 c4 d3 e3 f13

all subsets must be on the order of a'b'c'd'e'f

what is the method that can form all possible subsets combined of the given master array. and what are the statistical therories that are applied to this sience of data sorting

[dpb]

That's 16^6 = 16,777,216 combinations...each column has 16 choices for the next element having chosen the preceding.

It's combinations and permutations...

[Nourhan Elsayed]

yes, but combinations that are not in the order ''a,b,c,d,e,f,g ''are to be eleminated

[Ameer Hamza]

16^6 combinations exist after excluding non-''a,b,c,d,e,f,g'' combinations.

Answer 1

[Ameer Hamza]

This code shows how to generate all combinations as you mentioned in your question

M = rand(16, 6); % example

rows = cell(1,6);
[rows{:}] = ndgrid(1:16);
rows = cellfun(@(x) {x(:)}, rows);
rows = [rows{:}];
cols = repmat(1:6, size(rows,1), 1);
idx = sub2ind(size(M), rows, cols);

M_out = M(idx);

[Nourhan Elsayed]

thank you Ameer

it works

[Ameer Hamza]

I am glad to be of help!