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

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Manager
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I have posted this before. However, I use a manual method. I [#permalink]  12 Dec 2003, 04:48
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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.
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binomial theorem.jpg [ 17 KiB | Viewed 600 times ]

Director
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Maybe I'm being thick and missing something, but isn't it patently obvious that column B is greater?
Director
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On second reading, of course they are equal.
Director
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yep..both are equal.
Manager
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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
SVP
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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
Senior Manager
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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.
SVP
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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.
Director
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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.
Senior Manager
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I think stoolfi said it all ....

anand, if you want further explanation let me know and I shall try to explain more.
SVP
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Yes I need an explaination
SVP
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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.
Senior Manager
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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
Manager
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Revisiting an old problem:

So there is no other way but to do this manually?
_________________

Thanks!

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