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Distributing Objects

Date: 08/12/2001 at 14:09:14
From: ali khachan
Subject: Probability-counting

I need to know if there is a formula for distributing n 
indistinguishable objects into k indistinguishable urns.

Date: 08/12/2001 at 16:06:38
From: Doctor Anthony
Subject: Re: Probability-counting

This is the same as partitioning a number n into exactly k parts, but 
the result will vary, depending on whether empty urns are permitted.

You require the coefficient of x^n in the expansion of the generating 

    -------------------------------  if empty urns not permitted

or  -------------------------------  if empty urns are permitted

To be of practical use you really need a mathematics package like 
Maple or Mathcad, and you can then get the result in a few seconds.


In how many ways can 15 balls be distributed into 6 urns with no urn 

We require the coefficient of x^15 in the expansion of


Maple gives the term  26.x^15 and so we know there will be 26 ways 
that we could distribute 15 balls into 6 indistinguishable urns.

If empty urns are allowed, we require the coefficient of x^15 in the 
expansion of 

In this case Maple gives the term 110.x^15 and so there will be 110 
ways that 15 balls can be distributed into 6 urns with empty urns 
being permitted.

- Doctor Anthony, The Math Forum   
Associated Topics:
High School Permutations and Combinations

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