Combination of elements I have 3 subsets: A, B and C, each have 100 elements. How can I calculate how many combinations I can have of A B and C for a total of 100 elements in a new subset.
 A: From your clarification, it seems clear that You are asking for combinations, thus order doesn't matter, and that there must be at least $1$ each from $A,B,C$
This is easily solved by a version of  "stars and bars" which is explained  here (you need not see the ADDED portion)
Using the formula $\dbinom{n-1}{k-1}$,
the answer is  $\dbinom{100-1}{3-1} = \boxed{4851}$
A: From what I understand the question seems rather simple, so maybe a clarification on what you asked is needed, but for now: let's assume you don't care about order and there's no limits on how many elements from A, B or C you need to get every time, then we can consider a general total pool of $300$ elements. Since there are $\tbinom {n}{k}$ ways to choose an (unordered) subset of $k$ elements from a fixed set of $n$ elements, you're answer would be $\tbinom {300}{100}=4,158,251,463,258,564,744,783,383,526,326,405,580,280,466,005,743,648,708,663,033,658,000,000,000,000,000,000$
hope this helps
Edit1: the clarification made on the comments takes out the cases $0,0,100$ and $0,100,0$ and $100,0,0$. It is still not clear what happens when we reach $1,98,1$, if order is counted or not and if something like $2,2,96$ is possible...
