# I Configuration probability of partitioned objects

#### rabbed

With N objects, if I arrange each without replacement into K distinct partitions in which different object orders should not be accounted for:

- For distinct objects I get a total number of Wtot = K^N ways to partition them, and a specific distribution with N1 objects in partition 1, N2 objects in partition 2 etc. can be accomplished in W = N!/(N1!*N2!*...*NK) ways.

- For identical objects I get a total number of Wtot = (N+K-1)!/(N!*(K-1)!) ways to partition them, and a specific distribution with N1 objects in partition 1, N2 objects in partition 2 etc. can be accomplished in W = 1 way.

So the probabilities of a specific configuration in the two cases should be:

Pdistinct = N!/(N1!*N2!*...*NK) / K^N
Pidentical = 1 / ( (N+K-1)!/(N!*(K-1)!) )

Is this correct?

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