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Permutaion Combination Question

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skyfarer
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Permutaion Combination Question [#permalink] New post   01 Feb 2016, 18:09
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Hi, I have a question..

Suppose there are 100 people and there are 100 seats.. Then the possible arrangements are 100!
But if we have two rows or seats 50 each, what will be the number of possible arrangements in that case? is it 100!*2??



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Re: Permutaion Combination Question [#permalink] New post   02 Feb 2016, 11:06
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Hi skyfarer,

Unless you include some additional 'restrictions' to the prompt (or ask a question that is dependent on the fact that there are 2 rows), from a math standpoint, having two rows of 50 is no different from having one row of 100. The total number of permutations would still be 100!

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Re: Permutaion Combination Question [#permalink] New post   05 Feb 2016, 01:04
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skyfarer wrote:
Hi, I have a question..

Suppose there are 100 people and there are 100 seats.. Then the possible arrangements are 100!
But if we have two rows or seats 50 each, what will be the number of possible arrangements in that case? is it 100!*2??



ALTERNATE METHOD:

First you need to select students for first row which can be done in 100C50 ways

then you arrange selected 50 students in FIRST row in 50! ways
and
you arrange remaining 50 students in SECOND row in 50! ways

Total ways of arrangements = 100C50*50!*50!

I hope this helps!!!
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Re: Permutaion Combination Question [#permalink] New post   25 Feb 2016, 17:59
Thanks Rich and Bhoopendar,

I think I got it :) But Just wanted to verify once more.. So I think no matter how many fragments you do of this seating arrangements, answer would always be 100!
So the result would be same in all these cases (i.e. 100!)
1. 100 seats 1 row
2. 50 seats 2 rows
3. 25 seats 4 rows
4. 10 seats, 10 rows
5. Weird arrangement of four rows of 10, 20, 30 and 40 seats

So it means in any cinema hall, no matter how they have arranged the rows, if there are 100 seats, possible arrangements would always be 100! irrespective of rows and columns. Its so, right??

GMATinsight wrote:
skyfarer wrote:
Hi, I have a question..

Suppose there are 100 people and there are 100 seats.. Then the possible arrangements are 100!
But if we have two rows or seats 50 each, what will be the number of possible arrangements in that case? is it 100!*2??



ALTERNATE METHOD:

First you need to select students for first row which can be done in 100C50 ways

then you arrange selected 50 students in FIRST row in 50! ways
and
you arrange remaining 50 students in SECOND row in 50! ways

Total ways of arrangements = 100C50*50!*50!

I hope this helps!!!
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Re: Permutaion Combination Question [#permalink] New post   26 Feb 2016, 11:20
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Hi skyfarer,

Yes, assuming that every person can sit in any seat - and there are no special 'restrictions' - then the answer would always be 100!

GMAT assassins aren't born, they're made,
Rich



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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Re: Permutaion Combination Question [#permalink]
26 Feb 2016, 11:20
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