How many ways can I combine/group N items? Example of what I mean:
Items a,b,c: (abc) / (ab)(c) / (a)(bc) / (ac)(b) / (a)(b)(c) = 5 where parenthesis mean a group distinct in some way from the others.
Or for items a,b,c,d,e,f one might have: (ae)(b)(cdf)
In other words, all breakdowns, of variable group sizes.
(I did search, but either it hasn't been dealt with here or I do not know the correct mathematical terminology.)