Formula for combinations number with aggregation I've this scenario, 4 groups (as follow) with following values:


*

*Dimension A:


*

*A

*B


*Dimension B:


*

*K

*J

*L


*Dimension C:


*

*X

*Y


*Dimension D:


*

*F

*G



I want to know numbers all possible combinations, with aggregation.
So I want a result like this:


*

*A

*A K

*A K X

*A K X F

*A J

*A J X

*A J X F


and so on until the last


*

*B L Y G


I've though this formula to know the exact number of combinations:
Element DIM A * Element Dim B * Element DIM C * Element DIM D +
Element DIM A * Element Dim B * Element DIM C +
Element DIM A * Element Dim B +
Element DIM A

I want to know if this formula is correct and if exists an official formula for these cases.

If I understand your example correctly, your formula is correct. You're counting the number of ways of combining elements from the groups, one element from each group from the first group up to some final group, which can be any of the groups.
I don't think there are any "official" formulas in mathematics. As far as there is such a thing as officialness, I think "with aggregation" is not the official term for this.
