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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.
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. 
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.}
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