Given 'a' identical objects of one kind and 'b' identical objects of other kind. Also, given 'k' indistinguishable buckets. In how many ways can one put the '(a+b)' objects into the 'k' buckets such that every bucket has atleast a single object?
As an example, let's suppose we have 3 As and 2 Bs and we need to partition them into 2 buckets. (a=3, b=2, k=2). The possible combinations are:
- A | AABB
- AA | ABB
- AAA | BB
- AAAB | B
- AAB | AB
So, there exist 5 such partitions.