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m01 q24

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m01 q24 [#permalink] New post 24 Dec 2009, 13:24
If 5 noble knights are to be seated at a round table, then how many different ways can they be seated?



120
96
60
35
24


Can someone explain this to me?

Thanks so much
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Re: m01 q24 [#permalink] New post 26 Dec 2009, 11:00
sfeiner wrote:
If 5 noble knights are to be seated at a round table, then how many different ways can they be seated?



120
96
60
35
24


Can someone explain this to me?

Thanks so much


for a round table if we have n people then number of arrangements will be (n-1)!.
Its same as we fix one of the people and then (n-1) people can be seated in (n-1)! ways

so for 5 people we will have (5-1)!= 4! = 24

Ans E
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Re: m01 q24 [#permalink] New post 26 Dec 2009, 11:34
Just remember the formula-

N things/people can be arranged in straight line in N! ways

N things/people can be arranged in circular line in (N-1)! ways
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Re: m01 q24 [#permalink] New post 26 Dec 2009, 12:34
I assumed it would be N! but because its a circular table its (N-1)!? so 24?


So if the question had said 5 spots in a line it would be N! so 120 instead?

Sorry but I really didn't understand this

Thanks,

SF
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Re: m01 q24 [#permalink] New post 27 Dec 2009, 07:34
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Yes SF, had it been a straight line, the answer is N!,i.e.,120..just because question says it to be a circular table, answer is (N-1)!,i.e, 24.

I hope below explanation helps

Case1: Straight table.

5 people can sit like this, the first seat can be occupied by 5 knights, to occupy next seat there are only 4 knights, for third seat there are only 3 & so on.Multiply them all as it is 'AND' case.

5*4*3*2*1= 5!=120

Case 2: Circular table

It is difficult point out which is the first seat in a circular table.So we assume any one seat to be a first seat and one knight sits there. Now we have 4 seats and 4 knights to be arranged.Applying same logic as above.

i.e, second seat can be occupied by any 4 remaining knights,next seat by any 3 and so on.

4*3*2*1=4!=24

I hope now it's clear.
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Re: m01 q24 [#permalink] New post 27 Dec 2009, 13:03
Thanks!

That was really very clear, kudos.

SF
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Re: m01 q24 [#permalink] New post 04 Jan 2010, 01:33
Well, great work! You have helped me to improve my knowledge about this field. Thank you so much for sharing.
Re: m01 q24   [#permalink] 04 Jan 2010, 01:33
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