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From: wws@whuxlm.UUCP (Stoll W William)
Newsgroups: net.puzzle
Subject: Re: Balls and buckets combinatorics problem
Message-ID: <783@whuxlm.UUCP>
Date: Mon, 24-Jun-85 12:14:11 EDT
Article-I.D.: whuxlm.783
Posted: Mon Jun 24 12:14:11 1985
Date-Received: Tue, 25-Jun-85 07:51:49 EDT
References: <779@whuxlm.UUCP> <7306@watdaisy.UUCP>
Distribution: net
Organization: AT&T Bell Laboratories, Whippany
Lines: 33

> >   
> >   Given N balls and B buckets, how many ways can the balls be distributed
> >   among the buckets such that it is possible to find a bucket with at
> >   least K balls in it?  (K > 0, N >= K, B > 0)
> >   
> >   This problem was posed by a friend with values K == 65, N == 5000,
> >   and B == 100.  I have a text which answers the question "ways which
> >   result in E empty buckets", but I can't apply it to the above.
> >   Help is appreciated!
> >   
> >   Bill Stoll, ..!whuxlm!wws
> >   
> 	A more interesting and difficult problem is
> 		Given  N balls
> 		       M buckets
> 		Each bucket has a capacity to hold atmost B balls.
> 
> 	In how many ways can the balls be distributed among the buckets?
> 		{ Let it be denoted by F(N,M,B) }
> 
> 	[ Ofcourse  N <= M*B,
> 	  Buckets are numbered (distinguishable) and balls are not.]
> ------------------------------------
>
Ok, two questions:

1) What is F(N,M,B)?  I am still stuck.  If I could solve this, you are
   right, I could solve my original problem.
2) How is this problem more interesting than the original? :-)

Thanks for responding,

Bill Stoll, ..!whuxlm!wws