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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 1-to-1 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
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Re: 20 balls for 4 people

Quote:
 Originally Posted by tiba 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
Base 4 integer partion of 20. It should be easy to calculate for you.
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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