I am not doing this completely. Here are hints.
‘Groups’ in this context are subsets!
If there are N elements in a set, then there are 2<SUP>N</SUP> subsets of that set.
Now one of those sets is the empty set - the null-group no members.
There are N singletons set, subsets with only one element.
Now you combine those along with what you learned from the dice problem and finish it this off. Post your answer and we will check it.