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Permutation/Combination

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Permutation/Combination [#permalink] New post 20 May 2013, 12:49
There are 6 people models, 2 from Asia, 2 from Europe and 2 from America. How many ways can they arranged such that models from same continent are next to each other?? help please.
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Re: Permutation/Combination [#permalink] New post 20 May 2013, 13:42
AlfaTauri wrote:
There are 6 people models, 2 from Asia, 2 from Europe and 2 from America. How many ways can they arranged such that models from same continent are next to each other?? help please.


In this case, if you imagine the models in 6 chairs, sitting in blocks of 2, such the the models of the same continent are together.

The arrangement would look something like this diagrammatically:

_ _ | _ _ | _ _
B1 B2 B3

The arrangement can be {Asia,Europe,America} {Asia, America, Europe} ...... {America, Europe, Asia} {America, Asia, Europe} making it 6 distinct arrangements where the models can be seated next to each other if they are from the same continent.

Hope I am correct! :) Zarrlou Please do verify :)

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Re: Permutation/Combination [#permalink] New post 20 May 2013, 13:50
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Almost correct.

This part is correct

"The arrangement can be {Asia,Europe,America} {Asia, America, Europe} ...... {America, Europe, Asia} {America, Asia, Europe} making it 6 distinct arrangements where the models can be seated next to each other if they are from the same continent."

But not complete, every model of one country can switch chair with the other A,B or B,A for each case.

So you have to multiply 6 by 2 for each pair of chair , 6*2*2*2=48.

Hope it's clear
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Re: Permutation/Combination [#permalink] New post 20 May 2013, 13:55
My bad! :) I missed considering the fact that the models from the individual continents can change places between themselves ! :)

Thanks Zarrolou! :) The answer will be 48! :)

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Re: Permutation/Combination   [#permalink] 20 May 2013, 13:55
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