I've been struggling with a matlab problem of combinations and permutations for a while and came across your post here. I thought you might be able to help me out.
Let's say I have a vector say A =[1 2 3 4] and want to find every way I can choose all the elements of A to fit in some number of bins (let's say 3). Bin 1 could have (1, 2, 3), Bin 2 could have (4) or (0) and Bin 3 could have (4) or (0) as well. The problem isn't quite solved by "nchoosek" or "permpos" because each bin could have more or less elements than the previous bin and the element choice for each bin depends on the elements not already chosen. I know that the number of possible combinations is # of elements in A^#of bins (in this case 81), because I solved it out by hand. I am looking for an easier way to do this! I'm sorry if this sounds confusing!
If you can point me in the right direction or offer me any help I would greatly appreciate it!