A rather concise All Possible Combinations algorithm for Processing.

all_possible_combinations.pde

ArrayList<String> letters;
ArrayList<String> combo;
int n=6;
int k=n;

void go(int offset, int k) {
  if (k==0) {
    println(combo);
    return;
  }
  for (int i=offset; i<=letters.size()-k; ++i) {
    combo.add(letters.get(i));
    go(i+1, k-1);
    combo.remove(combo.size()-1);
  }
}

void setup() {
  letters = new ArrayList<String>();
  letters.add("a");
  letters.add("b");
  letters.add("c");
  letters.add("d");
  letters.add("e");
  letters.add("f");
  combo = new ArrayList<String>();
  for(int i=0; i<=k; i++){
    go(0, i);
  }
}