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# If 3 girls and 3 boys must sit in a row of six chairs but

Author Message
Manager
Joined: 14 May 2005
Posts: 82
Location: San Francisco
If 3 girls and 3 boys must sit in a row of six chairs but  [#permalink]

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15 Nov 2006, 19:45
1
00:00

Difficulty:

(N/A)

Question Stats:

100% (00:05) correct 0% (00:00) wrong based on 12 sessions

### HideShow timer Statistics

If 3 girls and 3 boys must sit in a row of six chairs but boys are not allowed to sit beside one another, how many different seating arrangements can be made?

(A) 12
(B) 36
(C) 72
(D) 180
(E) 720

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Manager
Joined: 10 Jul 2006
Posts: 67

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15 Nov 2006, 19:57
I think it's B:36

Imagine there are 6 seats __ __ __ __ __ __ . Let the boys seat in the first, third, and fifth seat. There are 3*2*1 arrangement for boys. For the second, fourth and sixth seats, apply the same logic, we have 6 arrangement for girls. So in total, there are 6*6 = 36 arrangement.
Senior Manager
Joined: 08 Jun 2006
Posts: 324
Location: Washington DC

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15 Nov 2006, 20:08
I think it is 72

In addition to the explanation of enola..
consider the case when Boys take 2nd, 4th and 6th and girls take 1st, 3rd 5th
Manager
Joined: 29 Aug 2006
Posts: 156

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15 Nov 2006, 20:20
It says boys dont sit next to each other, but girls can, right?
Isnt BGGBGB also a valid option?
Senior Manager
Joined: 05 Oct 2006
Posts: 258

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17 Nov 2006, 08:21
let 3 girls be seated in !3 ways..and in between them ,there r 4 places in which 3 boys have to be seated and that can be done by selecting 3 out of 4 places(4c3 ways) and filling the 3 boys in !3 ways...
hence !3 * 4c3 * !3 ways = 144

i dont know where i missed it.
what's the oa???

quote="Pokhran II"]If 3 girls and 3 boys must sit in a row of six chairs but boys are not allowed to sit beside one another, how many different seating arrangements can be made?

(A) 12
(B) 36
(C) 72
(D) 180
(E) 720[/quote]
VP
Joined: 28 Mar 2006
Posts: 1295

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17 Nov 2006, 17:15
AK47 wrote:
let 3 girls be seated in !3 ways..and in between them ,there r 4 places in which 3 boys have to be seated and that can be done by selecting 3 out of 4 places(4c3 ways) and filling the 3 boys in !3 ways...
hence !3 * 4c3 * !3 ways = 144

i dont know where i missed it.
what's the oa???

quote="Pokhran II"]If 3 girls and 3 boys must sit in a row of six chairs but boys are not allowed to sit beside one another, how many different seating arrangements can be made?

(A) 12
(B) 36
(C) 72
(D) 180
(E) 720
[/quote]

There are only 6 chairs so once 3 girls take 3 chairs the remaning 3 boys are left with 3 chairs only (though there are 4 spots available)

So 3!*3!*2 = 72
VP
Joined: 25 Jun 2006
Posts: 1084

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19 Nov 2006, 18:09
i also get 144. Can you explain it clearly, trivikram?

suppose the boys are already seated, and we insert the girls in between.

4 possibilities:

G B G B G B
B G B G B G
B G G B G B
B G B G G B

so i get: 3! * 3! * 4 = 144.
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 4851
Location: Singapore

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19 Nov 2006, 18:43
I"m getting 144 as well. Seems to be only 4 possibilites:

BGBGBG
GBGBGB
BGGBGB
BGBGGB
Non-Human User
Joined: 09 Sep 2013
Posts: 8848
Re: If 3 girls and 3 boys must sit in a row of six chairs but  [#permalink]

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25 Sep 2017, 19:05
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________
Re: If 3 girls and 3 boys must sit in a row of six chairs but &nbs [#permalink] 25 Sep 2017, 19:05
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