BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

seating arrangements

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 185
Joined: Thu Feb 04, 2010 3:06 am
Thanked: 6 times

seating arrangements

by gmatnmein2010 » Mon Feb 08, 2010 5:33 am
1. A family consisting of one mother, one father, two daughters and a son is taking a road trip in a sedan. The sedan has two front seats and three back seats. If one of the parents must drive and the two daughters refuse to sit next to each other, how many possible seating arrangements are there?
(A) 28
(B) 32
(C) 48
(D) 60
(E) 120


i took a lot of time and cud not solve it
pls suggest a short method
thanks
Top
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 1132
Joined: Mon Jul 20, 2009 3:38 am
Location: India
Thanked: 64 times
Followed by:6 members
GMAT Score:760

by harsh.champ » Mon Feb 08, 2010 6:02 am
gmatnmein2010 wrote:1. A family consisting of one mother, one father, two daughters and a son is taking a road trip in a sedan. The sedan has two front seats and three back seats. If one of the parents must drive and the two daughters refuse to sit next to each other, how many possible seating arrangements are there?
(A) 28
(B) 32
(C) 48
(D) 60
(E) 120


i took a lot of time and cud not solve it
pls suggest a short method
thanks
Case 1:-Only 1 parent driving+ 1 daughter in front seat . 2C1 x 2C1(selection of front seat daughter) x 3!(back seat arrangement)=24
Case 2 :-Both parents in the front seat. 2C1(for driver) x 2!(daughters arrangementson always sits in middle)=4
Ans. is 28.A
It takes time and effort to explain, so if my comment helped you please press Thanks button :)



Just because something is hard doesn't mean you shouldn't try,it means you should just try harder.

"Keep Walking" - Johnny Walker :P
Top
User avatar
Legendary Member
Posts: 1560
Joined: Tue Nov 17, 2009 2:38 am
Thanked: 137 times
Followed by:5 members

by thephoenix » Mon Feb 08, 2010 6:08 am
Total ways to seat them with one parent driving: 2 options for driver * 4 options for other seats = 2*4*3*2*1 = 48.
Assuming the 2 sisters do sit together, front seat we have 2 options for driver and 2 options for passenger (the other parent + son) = 4 ways.
Back seats: sisters sit together so either they sit in seats 1 and 2 or seats 2 and 3 = 2 ways. Also sisters themselves can sit in 2 ways so total = 2*2 = 4. So total ways sisters can sit together = 4*4 =16.
So ways they wont sit together = 48-16 = 32 ways.
Top
User avatar
Legendary Member
Posts: 1022
Joined: Mon Jul 20, 2009 11:49 pm
Location: Gandhinagar
Thanked: 41 times
Followed by:2 members

by shashank.ism » Mon Feb 08, 2010 6:12 am
gmatnmein2010 wrote:1. A family consisting of one mother, one father, two daughters and a son is taking a road trip in a sedan. The sedan has two front seats and three back seats. If one of the parents must drive and the two daughters refuse to sit next to each other, how many possible seating arrangements are there?
(A) 28
(B) 32
(C) 48
(D) 60
(E) 120


i took a lot of time and cud not solve it
pls suggest a short method
thanks
there can be two cases
Case 1: Only 1 parent driving + 1 daughter in front seat .
No. of combination= 2C1 x 2C1 x 3!=24
Case 2 : Both parents in the front seat. and in back seat girls will at extreme and son in between = 2C1 x 2!=4
Ans. is 28A
My Websites:
www.mba.webmaggu.com - India's social Network for MBA Aspirants

www.deal.webmaggu.com -India's online discount, coupon, free stuff informer.

www.dictionary.webmaggu.com - A compact free online dictionary with images.

Nothing is Impossible, even Impossible says I'm possible.
Top
Post new topic Post Reply
• Page 1 of 1