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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:

  1. A | AABB
  2. AA | ABB
  3. AAA | BB
  4. AAAB | B
  5. AAB | AB

So, there exist 5 such partitions.

  • 0
    Does the ordering withing the bucket matter (i.e. order in which the objects are put in the bucket)?2012-04-27
  • 0
    No, the ordering within the buckets doesn't matter.2012-04-27
  • 0
    I just saw your example. You say the buckets are different (distinguishable), but your example does not seem to make it so.2012-04-27
  • 0
    Sorry, I didn't meant different as in distinguishable. The buckets are indistinguishable.2012-04-28

2 Answers 2