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#1 2011-12-27 03:35:33
- juantheron
- Member
- Registered: 2011-10-19
- Posts: 312
no. of ways
In How Many Different Ways Can 12 Different Fruits Be Given Away To 3 Boys,
So That Each Boy Gets At Least One Fruit?
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#2 2011-12-27 07:22:44
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: no. of ways
Hi juan;
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#3 2011-12-28 04:21:59
- juantheron
- Member
- Registered: 2011-10-19
- Posts: 312
Re: no. of ways
yes bobbym thanks
but how can you get it
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#4 2011-12-28 09:55:13
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: no. of ways
Hi juan;
This is "a distinguishable balls into distinguishable urns problem."
There are two ways that I can think of.
1) A formula:
Where n is the number of distinguishable balls, k is the number of distinguishable boxes, r is the number of occupied boxes.
2) A generating function:
We are concerned with the coefficient of x^12, which we multiply by 12!.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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