question

Sure, a CTE. Construct a single field which contains the permutation, and then do a WHERE Perm NOT LIKE '%,' + N + ',%' (or something like that). Then filter it to the ones that are long enough (perhaps have a permlength field).

It reminds me of a palindrome puzzle that Itzik posed a while back. Adam Machanic, Steve Kass and I were deemed the "winners".

Edit to show code...

I've gone for the ordered variety as per a recent comment (it's also a bit easier potentially, as I'm checking the number on the front). My dbo.nums table goes from 1 to as high as you like. To make life interesting, I used items as just even numbers - ten of them. This gives 210 permutations, of 4 items out of 10. The first is 2,4,6,8. The last is 14,16,18,20. I unpivot the data so that it's configurable by setting the items CTE and by @numitems. I hope you like it. It didn't take long for me to throw together (maybe 5 minutes? - longer to write this paragraph I think). On my old machine, the code here was under one-second, but when I put 25 items and chose 6, it took a bit longer (26 seconds).

Also, to just count how many there are, I changed the final select to count out of permlist. This told me that there were 177100 entries for 6 from 25. It told me this in 6 seconds on my old machine. Of course, I could've worked this out much quicker using the original formula for this type of thing, as given at http://www.mathsisfun.com/combinatorics/combinations-permutations-calculator.html

7 out of 25 took 20 seconds to tell me there were 480700, and 8 took 51 seconds to tell me 1081575.

If order wasn't important, then I'd've done some different testing to see if I'd used the value before. If repetitions were allowed, I could've taken many different approaches.

There are better (faster) algorithms for doing this - I just went for simple. There are many heuristics that could be used to speed things up, such as not putting the smallest number on the front if there are more numbers to be added to the list.

declare @numitems int;
set @numitems = 4;

with items as
(select *
from dbo.nums
where num <= 20 and num % 2 = 0)
,
perms as 
(select cast(cast(num as binary(4)) as varbinary(max)) as perm, 1 as numentries
from items
union all
-- 'Prepend any that are smaller than the front value.'
select cast(n.num as binary(4)) + p.perm, p.numentries + 1
from perms p
join items n on n.num < cast(substring(perm,1,4) as int)
where p.numentries < @numitems
)
,permlist as
(
select 
   --'Arbitrary numbering. Order by perm if a proper order 
   --of permutations is required'
   row_number() over (order by (select 1)) as permnum, 
   perm
from perms
--'Permutations must be complete, not finishing early'
where numentries = @numitems
)
select 
   p.permnum,
   n.num as itemnum,
   cast(substring(p.perm,4*n.num-3,4) as int) as item
from permlist p
join dbo.nums n on n.num <= @numitems
;