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#1 2013-08-13 12:12:31

mathstudent2000
Member
Registered: 2013-07-26
Posts: 79

hockey stick identity problems

1.We have 8 pieces of strawberry candy and 7 pieces of pineapple candy. In how many ways can we distribute this candy to 4 kids?

2. In how many ways can we distribute 13 pieces of identical candy to 5 kids, if the two youngest kids are twins and insist on receiving an equal number of pieces?

3. 4 students are running for club president in a club with 50 members. How many different vote counts are possible, if everyone is required to vote?


Genius is one percent inspiration and ninety-nine percent perspiration

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#2 2013-08-13 14:16:09

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,161

Re: hockey stick identity problems

Hi;

Those can be handled with generating functions or solutions to a diophantine equation using x's and dashes.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#3 2013-08-13 15:36:28

mathstudent2000
Member
Registered: 2013-07-26
Posts: 79

Re: hockey stick identity problems

what is a diophantine equation?


Genius is one percent inspiration and ninety-nine percent perspiration

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#4 2013-08-13 15:42:06

mathstudent2000
Member
Registered: 2013-07-26
Posts: 79

Re: hockey stick identity problems

i solved no.2 but i need some hints on 1 and 3


Genius is one percent inspiration and ninety-nine percent perspiration

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#5 2013-08-13 20:35:57

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,161

Re: hockey stick identity problems

Hi;


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#6 2013-08-14 04:53:50

mathstudent2000
Member
Registered: 2013-07-26
Posts: 79

Re: hockey stick identity problems

for no.2 i tried it but its wrong


Genius is one percent inspiration and ninety-nine percent perspiration

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#7 2013-08-14 04:54:24

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,161

Re: hockey stick identity problems

Please verify 1 and 3 before we go any further.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#8 2013-08-14 04:56:01

mathstudent2000
Member
Registered: 2013-07-26
Posts: 79

Re: hockey stick identity problems

sorry, i mean no.3


Genius is one percent inspiration and ninety-nine percent perspiration

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#9 2013-08-14 04:57:08

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,161

Re: hockey stick identity problems

They said number 3 is wrong?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#10 2013-08-14 04:58:21

mathstudent2000
Member
Registered: 2013-07-26
Posts: 79

Re: hockey stick identity problems

yes


Genius is one percent inspiration and ninety-nine percent perspiration

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#11 2013-08-14 05:05:50

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,161

Re: hockey stick identity problems

Hi;
I see the problem, try this


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#12 2013-08-14 05:08:36

mathstudent2000
Member
Registered: 2013-07-26
Posts: 79

Re: hockey stick identity problems

thanks


Genius is one percent inspiration and ninety-nine percent perspiration

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#13 2013-08-14 05:09:48

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,161

Re: hockey stick identity problems

The problem was that I thought that each of the 4 students needed at least one vote. This is untrue, some could get 0 votes.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#14 2013-08-14 05:12:08

mathstudent2000
Member
Registered: 2013-07-26
Posts: 79

Re: hockey stick identity problems

got it


Genius is one percent inspiration and ninety-nine percent perspiration

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