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# In how many arrangements can a teacher seat 3 girls and 4

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Senior Manager
Joined: 25 Nov 2006
Posts: 298
Schools: St Gallen, Cambridge, HEC Montreal
In how many arrangements can a teacher seat 3 girls and 4  [#permalink]

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28 Nov 2007, 11:08
1
00:00

Difficulty:

(N/A)

Question Stats:

88% (00:41) correct 12% (01:50) wrong based on 182 sessions

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In how many arrangements can a teacher seat 3 girls and 4 boys in a row of 7 seats if the girls are to have the secon, fourth and sixth seats?

(A) 12
(B) 36
(C) 144
(D) 288
(E) 5,040

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CEO
Joined: 17 Nov 2007
Posts: 2913
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

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28 Nov 2007, 11:25
C.

for girls: p=3*2*1=6
for boys: q=4*3*2*1=24

together: p*q=6*24=144
CEO
Joined: 17 Nov 2007
Posts: 2913
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

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28 Nov 2007, 11:32
rajpdsouza, GOOD LUCK on tomorrow exam!!!
Senior Manager
Joined: 26 Jul 2007
Posts: 357

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28 Nov 2007, 11:33
walker wrote:
rajpdsouza, GOOD LUCK on tomorrow exam!!!

Thanks! Although my post count is low, I have been a daily lurker since I joined. Hopefully, another gmatclubber will join the 700-ranks.
SVP
Joined: 29 Mar 2007
Posts: 1648

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28 Nov 2007, 11:35
lumone wrote:
In how many arrangements can a teacher seat 3 girls and 4 boys in a row of 7 seats if the girls are to have the secon, fourth and sixth seats?

(A) 12
(B) 36
(C) 144
(D) 288
(E) 5,040

BGBGBGB Girls can be places in 3! ways and boys can be placed in 4! ways. so 3!*4!=144.

C
Intern
Joined: 12 Aug 2008
Posts: 8

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27 Aug 2008, 01:43
This is another reasonable solution:

On seat one you can put any of the 4 boys, on seat two you can put any of the 3 girls, on seat 3 you can put any of the remaining 3 boys, on seat four you can put any of the remaining 2 girls, seat five you can put any of the remaining 2 boys, and on seats six and seven you can put the one remaining girl and boy. You can write this representation in the following form:

4x3x3x2x2x1x1 = 144
Manager
Joined: 27 Oct 2008
Posts: 125

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27 Sep 2009, 21:37
In how many arrangements can a teacher seat 3 girls and 4 boys in a row of 7 seats if the girls are to have the secon, fourth and sixth seats?

(A) 12
(B) 36
(C) 144
(D) 288
(E) 5,040

Soln: 4! * 3! ways
= 144

Ans is C
Manager
Joined: 22 Dec 2009
Posts: 225

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16 Feb 2010, 12:00
lumone wrote:
In how many arrangements can a teacher seat 3 girls and 4 boys in a row of 7 seats if the girls are to have the secon, fourth and sixth seats?

(A) 12
(B) 36
(C) 144
(D) 288
(E) 5,040

BGBGBGB

G can be arranged in 3! ways
B can be arranged in 4! ways

Therefore 3! x 4! = 144

--== 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: Permutation Question   [#permalink] 16 Feb 2010, 12:00