There's a game called Kakuro (Wikipedia page here: http://en.wikipedia.org/wiki/Kakuro ) that uses 'how many x digit combinations add up to y.' There are many tables for those combinations online (example: http://www.brainbashers.com/combinations.asp ).
What you're looking for is in the section for 4-digit combinations, in the row for 27.
If order doesn't matter (1234 is the same as 1243), there are only 3 combinations: 3789, 4689, and 5679.
If order does matter (1234 is different than 1243), there are 72 combinations:
24 combinations using 3789:
3789
3798
3879
3978
3897
3987
7389
7398
7839
7938
7893
7983
8379
8397
8739
8937
8793
8973
9378
9387
9738
9837
9783
9873
Another 24 combinations using 4689. . .
And another 24 combinations using 5679. . .