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#1 2016-07-03 01:12:42

mathster
Member
Registered: 2015-10-09
Posts: 15

Problem.

Hi, I'm struggling with the following problem:

There are 5 boys and 4 girls in my class. All of them are distinguishable.
In how many ways can they be seated in a row of 9 chairs such that at least 3 girls are all next to each other?

Please help. Thanks in advance.

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#2 2016-07-03 10:47:44

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

Re: Problem.

Hi;


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 2016-07-03 16:27:06

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

Re: Problem.


{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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#4 2016-07-05 00:02:50

mathster
Member
Registered: 2015-10-09
Posts: 15

Re: Problem.

I'm torn between two different answers, if possible, could you please provide a solution on how you got them?

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#5 2016-07-05 00:18:49

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

Re: Problem.

Take a third opinion.
You will be torn among three different answers.

Last edited by thickhead (2016-07-05 00:25:01)


{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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#6 2016-07-05 04:51:12

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

Re: Problem.


{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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#7 2016-07-05 07:17:47

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

Re: Problem.

I'm torn between two different answers, if possible, could you please provide a solution on how you got them?

You do not have the right answer?


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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#8 2016-07-06 22:52:49

mathster
Member
Registered: 2015-10-09
Posts: 15

Re: Problem.

thickhead wrote:

I get it now. But one thing you didn't include: When 4 girls sit together it should be N3=4!(ways to arrange the girls)*6!(5 boys and the 4-girl block).
So N1+N2+N3=103680.
So bobbym was right. neutral
Thanks anyway, though.

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#9 2016-07-07 00:04:02

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

Re: Problem.

thank you,Mathster. it was an aberration on my part.


{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.}

Offline

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