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June 20th, 2012, 02:17 AM   #1
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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
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June 20th, 2012, 03:51 AM   #2
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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?
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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!
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June 20th, 2012, 04:29 AM   #4
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Re: 20 balls for 4 people

Hint: ways = (n+1)(n+2)(n+3) / k
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