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**Mathegocart****Member**- Registered: 2012-04-29
- Posts: 1,900

Consider a set A that has [1,2,3,4,5,6,7,8,9,10,11,12,13,14], now 4 integers are taken from that set to create a new set, B. What is the probability that the first 2 digits summed together is greater than the last 2 digits summed together?

The integral of hope is reality.

May bobbym have a wonderful time in the pearly gates of heaven.

He will be sorely missed.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi mathgogocart;

The first condition that you must always include in problems like these is whether there is replacement or not. I will assume that there is not.

This is similar to the "Lucky Tickets Problem" and is solved using generating functions or programming. I am getting 203 / 429

**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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**Mathegocart****Member**- Registered: 2012-04-29
- Posts: 1,900

Would Python be suitable for that?

The integral of hope is reality.

May bobbym have a wonderful time in the pearly gates of heaven.

He will be sorely missed.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Of course, but M is much better. M allows you to combine math and programming in a natural sort of way.

**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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**thickhead****Member**- Registered: 2016-04-16
- Posts: 1,086

I have verified bobbym's result indirectly. I do not have exotic resources but with pen,paper and to a very less extent calculator I did the work. I estimated sample space of 2 numbers with same total and paired them on first 2 and next to places. the result is 1288 cases out of 14P4 give equality of sum of 1st two numbers to sum of 3rd and 4th numbers.This is 23/429. The remaining probabilty is equally divided between > and < conditions. So the required probability =(429-23)/429 X 1/2 =203/429.

**{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha{Gods rejoice at those places where ladies are respected.}**

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