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June 20th, 2012, 02:17 AM  #1 
Member Joined: Jan 2012 Posts: 52 Thanks: 0  20 balls for 4 people
Hello, can someone please help me with this one? In how many different ways 20 equal balls can be given to 4 people?  A situation where someone receives no ball IS valid.  All the 20 balls must be given. Thanks 
June 20th, 2012, 03:51 AM  #2 
Member Joined: Jun 2012 From: UK Posts: 39 Thanks: 0  Re: 20 balls for 4 people
Consider a string of 23 items, consisting of 20 balls, and 3 dividers. The three dividers divide your string up into 4 segments, one for each of the people. There is no a 1to1 correspondence between an arrangement of the items, and allocation of balls to the 4 people. So your question boils down to how many arrangements are there of 23 items of which 3 are of one type and 20 are of another type. Can you finish it from there? 
June 20th, 2012, 03:57 AM  #3  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: 20 balls for 4 people Quote:
and I think this is number theory math!  
June 20th, 2012, 04:29 AM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,146 Thanks: 1003  Re: 20 balls for 4 people
Hint: ways = (n+1)(n+2)(n+3) / k


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