Where a group can consist of 1 or more items, groups don't have to be equally sized and items can be duplicates. Example - Choose 3 groups:
Items: 1 2 2 3
Groups:
(1) (2 2) (3)
(1 2) (2) (3)
(3 1) (2) (2)
(3 2) (2) (1)
Update Following Rasmus' comment, I see that this is more technically described as finding the possible partitions of a multiset where the number of cells is x.