You are asking about "permutations" here, not "combinations".  A
permutation is the same items in a different order, as you have shown.
A combination is a different selection from the group of items.
Combinations would be:

1:  3, 7
2:  3, 21
3:  21
4:  3, 7, 21
etc.

Try googling for "permutation algorithm"

rossum

As far as i know Robert Sedgewick had an article on permutation on his
website,
maybe searching http://www.cs.princeton.edu/~rs/ might be helpful.

best regards
Markus Tazl

You have combinations and permutations confused.

See http://mindprod.com/jgloss/permutation.html
http://mindprod.com/jgloss/combination.html
--

Roedy Green Canadian Mind Products
The Java Glossary
http://mindprod.com

 As others already have explained, these are not combinations,
 but permutations.

 Permutations are a part of the library »ram.jar«:

public class Main
{ public static void main( final java.lang.String[] args )  
 { java.lang.Object[] hand = new java.lang.Object[]{ "T", "H", "E"  };
   for
   ( final java.lang.Object[] p :
     new de.dclj.ram.system.iteration.Permutations( hand ))
   java.lang.System.out.print( java.util.Arrays.toString( p )); }}

[T, H, E][T, E, H][H, T, E][H, E, T][E, T, H][E, H, T]

http://www.purl.org/stefan_ram/pub/ram-jar