My Math Forum very hard question

 October 28th, 2010, 01:21 PM #1 Member   Joined: Oct 2010 Posts: 30 Thanks: 0 very hard question could someone help with this please, Let k be a non-negative integer. How many distinct integer-valued 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, 01:52 PM #2 Newbie   Joined: Oct 2010 Posts: 17 Thanks: 0 Re: very hard question I think it´s ${n-rk+r-1}\choose{r-1}$
 November 2nd, 2010, 02:20 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 $n\,\geq\,rk.$
 November 3rd, 2010, 04:59 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, 06:22 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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