Placing 6 items in 3 different boxes

I need to group 6 items in different three boxes. Any combination shall be possible, even empty boxes are allowed. How can I write a code to find all the possible combinations?

Answer 1

[Akira Agata]

Like this?

N1, N2 and N3 are possible combination of select k out of 6 items for 1st box, l out of 6-k items for 2nd box and 6-k-l out of 6-k-l items for 3rd box. Note that N3 is always 1.

Nall = 0;
for k = 0:6
N1 = nchoosek(6,k);
  for l = 0:6-k
    N2 = nchoosek(6-k,l);
    N3 = nchoosek(6-k-l,6-k-l);
    Nall = Nall + N1*N2*N3;
  end
end

The answer is:

>> Nall
Nall =
 729