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

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

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15 Nov 2006, 20:45
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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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Joined: 10 Jul 2006
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15 Nov 2006, 20:57
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.
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15 Nov 2006, 21:08
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
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15 Nov 2006, 21:20
It says boys dont sit next to each other, but girls can, right?
Isnt BGGBGB also a valid option?
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17 Nov 2006, 09:21
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]
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17 Nov 2006, 18:15
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
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19 Nov 2006, 19:09
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.
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19 Nov 2006, 19:43
I"m getting 144 as well. Seems to be only 4 possibilites:

BGBGBG
GBGBGB
BGGBGB
BGBGGB
19 Nov 2006, 19:43
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