Combination of one of every string group in all possible combinations and orders in matlab - string

Question

So I forgot a string and know there is three substrings in there and I know a few possibilities for each string. So all I need to do is go through all possible combinations and orders until I find the one I forgot. But since humans can only hold four items in their working memory (definately an upper limit for me), I cant keep tabs on which ones I examined.
So say I have n sets of m strings, how do I get all strings that have a length of n substrings consisting of one string from each set in any order?
I saw an example of how to do it in a nested loop but then I have to specify the order. The example is for n = 3 with different m`s. Not sure how to make this more general:
first = {'Hoi','Hi','Hallo'};
second = {'Jij','You','Du'};
third = {'Daar','There','Da','LengthIsDifferent'};
for iF = 1:length(first)
for iS = 1:length(second)
for iT = 1:length(third)
[first{iF}, second{iS}, third{iT}]
end
end
end
About this question: it does not solve this problem because it presumes that the order of the sets to choose from is known.

Answer 1

This generates the cartesian product of the indices using ndgrid.
Then uses some cellfun-magic to get all the strings. Afterwards it just cycles through all the permutations and appends those.
first = {'Hoi','Hi','Hallo'};
second = {'Jij','You','Du'};
third = {'Daar','There','Da','LengthIsDifferent'};
Vs = {first, second, third};
%% Create cartesian product
Indices = cellfun(#(X) 1:numel(X), Vs, 'uni', 0);
[cartesianProductInd{1:numel(Vs)}] = ndgrid(Indices{:});
AllStringCombinations = cellfun(#(A,I) A(I(:)), Vs, cartesianProductInd,'uni',0);
AllStringCombinations = cat(1, AllStringCombinations{:}).';%.'
%% Permute what we got
AllStringCombinationsPermuted = [];
permutations = perms(1:numel(Vs));
for i = 1:size(permutations,1)
AllStringCombinationsPermuted = [AllStringCombinationsPermuted; ...
AllStringCombinations(:,permutations(i,:));];
end