Java Program to generate combination

If one wants to generate various possible combinations ( order doesn't matter) from char array.
Ex:
For input {'a','b'},  output would be 'a','b','ab'
For input {'a','b','c'} , output would be 'a','b','c','ac','ab','bc','ac', 'abc'

import java.util.HashSet;
import java.util.Iterator;
import java.util.Set;
import java.util.Vector;

public class AllComb {
          static char arr[] = {'a','b','c','d'};

          public static void main(String args[]) {
                Vector<String> wordSet = new Vector<String>();
                wordSet.add("");
                for (int i=0;i<arr.length;i++){
                        int vectorSize = wordSet.size();
                        for (int index=0;index<vectorSize;index++){
                                String str = wordSet.get(index) + arr[i];
                                wordSet.add(str);
                        }
  
                   }
 
               int vectorSize = wordSet.size();
              for (int index=0;index<vectorSize;index++){
                   System.out.println( wordSet.get(index));
              }
        }
}