Your various examples and descriptions seem a bit inconsistent to me, so I am probably misunderstanding something. None the less, the following appears to do what your last example does, without the hard coded nested loops. It could easily be modified for different combinations of combinations and variations (ouch!)

This produces the following (abridged)

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Cardinality: 1
( ( A ),( A ) )
( ( A ),( B ) )
( ( A ),( C ) )
( ( A ),( D ) )
( ( A ),( E ) )
( ( A ),( F ) )
( ( B ),( A ) )
( ( B ),( B ) )
( ( B ),( C ) )
( ( B ),( D ) )
( ( B ),( E ) )
( ( B ),( F ) )
( ( C ),( A ) )
( ( C ),( B ) )
( ( C ),( C ) )
( ( C ),( D ) )
( ( C ),( E ) )
( ( C ),( F ) )
( ( D ),( A ) )
( ( D ),( B ) )
( ( D ),( C ) )
( ( D ),( D ) )
( ( D ),( E ) )
( ( D ),( F ) )
( ( E ),( A ) )
( ( E ),( B ) )
( ( E ),( C ) )
( ( E ),( D ) )
( ( E ),( E ) )
( ( E ),( F ) )
( ( F ),( A ) )
( ( F ),( B ) )
( ( F ),( C ) )
( ( F ),( D ) )
( ( F ),( E ) )
( ( F ),( F ) )
Cardinality: 2
( ( A,B ),( A,B ) )
( ( A,B ),( A,C ) )
( ( A,B ),( A,D ) )
( ( A,B ),( A,E ) )
( ( A,B ),( A,F ) )
( ( A,B ),( B,C ) )
( ( A,B ),( B,D ) )
( ( A,B ),( B,E ) )
( ( A,B ),( B,F ) )
( ( A,B ),( C,D ) )
( ( A,B ),( C,E ) )
( ( A,B ),( C,F ) )
( ( A,B ),( D,E ) )
( ( A,B ),( D,F ) )
( ( A,B ),( E,F ) )
( ( A,C ),( A,B ) )
( ( A,C ),( A,C ) )
( ( A,C ),( A,D ) )
( ( A,C ),( A,E ) )
( ( A,C ),( A,F ) )
( ( A,C ),( B,C ) )
( ( A,C ),( B,D ) )
( ( A,C ),( B,E ) )
( ( A,C ),( B,F ) )
( ( A,C ),( C,D ) )
( ( A,C ),( C,E ) )
( ( A,C ),( C,F ) )
( ( A,C ),( D,E ) )
( ( A,C ),( D,F ) )
( ( A,C ),( E,F ) )
( ( A,D ),( A,B ) )
( ( A,D ),( A,C ) )
( ( A,D ),( A,D ) )
...
Cardinality: 3
( ( A,B,C ),( A,B,C ) )
( ( A,B,C ),( A,B,D ) )
( ( A,B,C ),( A,B,E ) )
( ( A,B,C ),( A,B,F ) )
( ( A,B,C ),( A,C,D ) )
( ( A,B,C ),( A,C,E ) )
( ( A,B,C ),( A,C,F ) )
( ( A,B,C ),( A,D,E ) )
( ( A,B,C ),( A,D,F ) )
( ( A,B,C ),( A,E,F ) )
( ( A,B,C ),( B,C,D ) )
( ( A,B,C ),( B,C,E ) )
( ( A,B,C ),( B,C,F ) )
( ( A,B,C ),( B,D,E ) )
( ( A,B,C ),( B,D,F ) )
( ( A,B,C ),( B,E,F ) )
( ( A,B,C ),( C,D,E ) )
( ( A,B,C ),( C,D,F ) )
( ( A,B,C ),( C,E,F ) )
( ( A,B,C ),( D,E,F ) )
( ( A,B,D ),( A,B,C ) )
( ( A,B,D ),( A,B,D ) )
( ( A,B,D ),( A,B,E ) )
( ( A,B,D ),( A,B,F ) )
( ( A,B,D ),( A,C,D ) )
( ( A,B,D ),( A,C,E ) )
( ( A,B,D ),( A,C,F ) )
( ( A,B,D ),( A,D,E ) )
( ( A,B,D ),( A,D,F ) )
( ( A,B,D ),( A,E,F ) )
( ( A,B,D ),( B,C,D ) )
( ( A,B,D ),( B,C,E ) )
( ( A,B,D ),( B,C,F ) )
( ( A,B,D ),( B,D,E ) )
( ( A,B,D ),( B,D,F ) )
( ( A,B,D ),( B,E,F ) )
( ( A,B,D ),( C,D,E ) )
( ( A,B,D ),( C,D,F ) )
( ( A,B,D ),( C,E,F ) )
( ( A,B,D ),( D,E,F ) )
( ( A,B,E ),( A,B,C ) )
( ( A,B,E ),( A,B,D ) )
( ( A,B,E ),( A,B,E ) )
( ( A,B,E ),( A,B,F ) )
( ( A,B,E ),( A,C,D ) )
( ( A,B,E ),( A,C,E ) )
( ( A,B,E ),( A,C,F ) )
( ( A,B,E ),( A,D,E ) )
( ( A,B,E ),( A,D,F ) )
( ( A,B,E ),( A,E,F ) )
( ( A,B,E ),( B,C,D ) )
( ( A,B,E ),( B,C,E ) )
( ( A,B,E ),( B,C,F ) )
( ( A,B,E ),( B,D,E ) )
( ( A,B,E ),( B,D,F ) )
( ( A,B,E ),( B,E,F ) )
( ( A,B,E ),( C,D,E ) )
( ( A,B,E ),( C,D,F ) )
( ( A,B,E ),( C,E,F ) )
( ( A,B,E ),( D,E,F ) )
( ( A,B,F ),( A,B,C ) )
( ( A,B,F ),( A,B,D ) )
( ( A,B,F ),( A,B,E ) )
( ( A,B,F ),( A,B,F ) )
( ( A,B,F ),( A,C,D ) )
( ( A,B,F ),( A,C,E ) )
( ( A,B,F ),( A,C,F ) )
( ( A,B,F ),( A,D,E ) )
( ( A,B,F ),( A,D,F ) )
( ( A,B,F ),( A,E,F ) )
( ( A,B,F ),( B,C,D ) )
( ( A,B,F ),( B,C,E ) )
( ( A,B,F ),( B,C,F ) )
( ( A,B,F ),( B,D,E ) )
( ( A,B,F ),( B,D,F ) )
( ( A,B,F ),( B,E,F ) )
( ( A,B,F ),( C,D,E ) )
( ( A,B,F ),( C,D,F ) )
( ( A,B,F ),( C,E,F ) )
( ( A,B,F ),( D,E,F ) )
...
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