Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 9/18/84 exptools; site whuxlm.UUCP Path: utzoo!watmath!clyde!burl!ulysses!allegra!whuxlm!wws 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