Java String array getting all combinations based on n!/r!(n-r)!

Question

I have tried to search about it, but have not found a definitive answer yet. I am trying to write a program which compares a string array against all combinations of another string array, but these combinations have the same number of elements as the previous array. To explain better, lets say I have two string arrays, n = {alpha,beta,gamma,delta,epsilon} and r ={beta,gamma,delta}. Now what I want to do is, get all combinations (of three strings in each combination) from the set 'n' and compare the set 'r' against them all. If I get a match, then perform some action. I am aware that to get all combinations, I need to apply the formula,

                            nCr = n!/r!(n-r)!   (where 0<=r<=n)

in my case, n = 5, and r = 3, which gives 10 combinations in total. I need to generate all these combinations(10 in this case) and compare them against the array 'r'. I do not have a starting point yet, and I do not expect to get an answer but a little light towards how it can be implemented (will be probably done recursively?) would be great! Thanks in advance.

Answer 1

Given the additional context you've provided in the comments, here's what I'd suggest.

Turn n into a set for easier querying:

String[] n = {"alpha", "beta", "gamma", "delta", "epsilon"};
Set<String> nset = new HashSet<String>();
nset.addAll(Arrays.asList(n));

Now you can check if it contains all the elements of r :

String[] r = {"beta", "gamma", "delta"};
if (nset.containsAll(Arrays.asList(r))) {
  // do something
}

This can be repeated with multiple different r arrays, and it will be more efficient than iterating over all the possible subsets of n and comparing them with a particular r .