Say I have n items. How can I find the amount of combinations possible of subset sets covering all items, when order does not matter. This is maybe badly worded, so allow me to give an example:
n=3, so we have items A,B, and C.
All possible subset sets covering all items would be
- [A B C]
- [A BC]
- [AC B]
- [AB C]
That makes for 5 possibilities.
Say the function to calculate this is
f(n) and the total amount of subsets in all sets is
g(n) (that would mean g(3) as in the example is 10). I managed to figure out
f(n)=f(n-1)+g(n-1). However, this is where I am kind of stuck.