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# There are 2 brothers among a group of 20 persons. In how

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Director
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There are 2 brothers among a group of 20 persons. In how [#permalink]  08 Nov 2005, 11:41
There are 2 brothers among a group of 20 persons. In how many ways can the group be arranged around a circle so that there is exactly one person between the two brothers?

(a) 2 * 19!
(b) 18! * 18
(c) 19! * 18
(d) 2 * 18!
(e) 17*18!
Manager
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bewakoof wrote:
18*18!

Could you explain, bewakoof?
Thanks. This is my weak area.
Director
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celiaXDN wrote:
bewakoof wrote:
18*18!

Could you explain, bewakoof?
Thanks. This is my weak area.

I hope I am right.. but i have been making very silly mistakes today..

there has to be exactly one person between these two brothers.. so, there are 18 other people who can be in this position..

since this is a circular probability how many ways these 18 people can be arranged.. since the two brothers will have to retain the same spots.. 18!..
so the total combined possibilities are 18*18!.
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Manager
Joined: 15 Aug 2005
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Location: New York
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bewakoof wrote:
celiaXDN wrote:
bewakoof wrote:
18*18!

Could you explain, bewakoof?
Thanks. This is my weak area.

I hope I am right.. but i have been making very silly mistakes today..

there has to be exactly one person between these two brothers.. so, there are 18 other people who can be in this position..

since this is a circular probability how many ways these 18 people can be arranged.. since the two brothers will have to retain the same spots.. 18!..
so the total combined possibilities are 18*18!.

Thanks, so can I interpret it as this:

Once a guy is chosen for the position between the two brothers, the three of them remain a fixture, plus the other 17 guys, we also have 18 positions. The change of positions between the two brothers doesnâ€™t matter, right?
Director
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Re: Arrange persons in circle [#permalink]  08 Nov 2005, 13:37
OA is D 2*18!

here is the explanation.
Let us assume that 2 brother and one person in between them as single entity. So total no of objects to arrange now are = 20 â€“ 2 â€“1 + 1

(considering those 3 as one) = 18
Circular combination of arranging 18 object is = (18 â€“1)! = 17!

Now each of the other 18 person can come in between those 2 brothers, so total no of ways = 18 * 17!
Now 2 brother can switch there seat in 2 ways. Hence total no of ways = 2*18*17!= 2*18!

cool_jonny009 wrote:
There are 2 brothers among a group of 20 persons. In how many ways can the group be arranged around a circle so that there is exactly one person between the two brothers?

(a) 2 * 19!
(b) 18! * 18
(c) 19! * 18
(d) 2 * 18!
(e) 17*18!
Manager
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Re: Arrange persons in circle [#permalink]  08 Nov 2005, 14:02
cool_jonny009 wrote:
OA is D 2*18!

here is the explanation.
Let us assume that 2 brother and one person in between them as single entity. So total no of objects to arrange now are = 20 â€“ 2 â€“1 + 1

I dont get this step. So 20 places to assign, we treat the brothers as fixed, and a 3rd person in between them as fixed. 20-2=18 right?
why do you write 20-2-1+1? whats the +1 for?
VP
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Re: Arrange persons in circle [#permalink]  08 Nov 2005, 14:12
nero44 wrote:
cool_jonny009 wrote:
OA is D 2*18!

here is the explanation.
Let us assume that 2 brother and one person in between them as single entity. So total no of objects to arrange now are = 20 â€“ 2 â€“1 + 1

I dont get this step. So 20 places to assign, we treat the brothers as fixed, and a 3rd person in between them as fixed. 20-2=18 right?
why do you write 20-2-1+1? whats the +1 for?

You came up with same thing as OE says. Just that OE explanation is more detailed.

all its saying is that: treat 2 brother and a person between themas 1.
if we remove all three we have: 20 - 3 = 17 people. Now as we are considering 3 people as 1, add 1 to get total number of people to consider: 17 + 1 = 18
Manager
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aaaaaaaaaaaaahhh, I just got enlightened!!! Big thx!
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