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October 28th, 2010, 02:21 PM  #1 
Member Joined: Oct 2010 Posts: 30 Thanks: 0  very hard question
could someone help with this please, Let k be a nonnegative integer. How many distinct integervalued vectors (n1, n2, . . . , nr) are there which satisfy both of the following constraints? • nj ?k for all j=1,2,...,r and • n1 + n2 + · · · + nr = n. 
November 2nd, 2010, 02:52 PM  #2 
Newbie Joined: Oct 2010 Posts: 17 Thanks: 0  Re: very hard question
I think it´s 
November 2nd, 2010, 03:20 PM  #3 
Senior Member Joined: May 2008 From: York, UK Posts: 1,300 Thanks: 0  Re: very hard question
Yes, that's right. Clearly only makes sense for 
November 3rd, 2010, 05:59 PM  #4 
Member Joined: Oct 2010 Posts: 30 Thanks: 0  Re: very hard question
how do you get to that solution. i dont uinderstnad the working leading up to it :S

November 3rd, 2010, 07:22 PM  #5 
Newbie Joined: Jul 2010 Posts: 5 Thanks: 0  Re: very hard question
Consider it this way. You have n balls, you have to put them in r bins. Each bin must have k balls, that leaves n  rk balls to distribute. There are r bins to put them in. This is now a simplified partition problem. 

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