I have posted this before. However, I use a manual method. I

Question

I have posted this before. However, I use a manual method.
I think there might be a binomial theorem method, and I wonder
if someone can point out. Thanks.

The question is Column A >, < or = to Coulmn B.

stoolfi · Answer

Maybe I'm being thick and missing something, but isn't it patently obvious that column B is greater?

stoolfi · Answer

On second reading, of course they are equal.

dj · Answer

yep..both are equal.

tzec76 · Answer

Yes. Both are them are equal.

I used this method, and I wondering if there is a binomial theorem
or simpler method to it.

Column A 

3+3+1 
3+2+2 
3+1+3 


Column B 

1+3+3 
1+2+4 
1+1+5

anandnk · Answer

Combinations for Column A 

Persons -> p1 p2 p3 
 3 1 3
 3 2 2
 3 3 1
 1 3 3
 2 3 2
 2 2 3
-----------------------
total = 6

Combinations for Column B
Persons -> p1 p2 p3 
 1 1 5
 1 2 4
 1 3 3
 1 4 2
 1 5 1
 2 1 4
 2 2 3
 2 3 2
 2 4 1
 3 1 3
 3 2 2
 3 3 1
 4 1 2
 4 2 1
 5 1 1
------------------------
total = 15
I think B > A

pitts20042006 · Answer

anand ...

why wouldn't you have the combinations you have under B, eg. 115 or 511 and similar, under A?? all the combinations under B satisfy the criteria for A and vice versa and so they are both equal.

anandnk · Answer

Your question completely went over my head. Are you saying combination 115 is same as 511. I believe they should be different.
Also I thought under rule A one person should receive atleast $3 and under B one person should receive atleast $1. If not so then I have not understood the question corectly.
Please clarify.

stoolfi · Answer

tzec--

Why use any theorem? Common sense should tell you that there's no way that the money can be distributed without at least someone getting $3...

Of course, it took me a minute, but in retrospect, it's terribly obvious.

pitts20042006 · Answer

I think stoolfi said it all ....

anand, if you want further explanation let me know and I shall try to explain more.

anandnk · Answer

Yes I need an explaination

anandnk · Answer

Please accept my apologies. I thought total of seven dollars have to be distributed instead of seven one dollar bills. What a terrible mistake. It is 11:40 PM after doing reading comprehension on humanities and literature.
You know how it can be to a science/engineering person. I need to sleep now.

pitts20042006 · Answer

yup I know how it is. It's 11:40 pm after a long hard work week for me too

And definitely NO need for any apologies at all ... explanations and sharing is what this forum is all about. Have a good weekend

.. and enjoy India's good batting form in the ongoing test match .. if you follow cricket

rchadha · Answer

Revisiting an old problem:

So there is no other way but to do this manually?

I have posted this before. However, I use a manual method. I

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