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

Redeem

seating. source: manhattan

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 50
Joined: Sun Apr 04, 2010 7:28 am
Followed by:1 members

seating. source: manhattan

by jsasipriya » Sun Aug 01, 2010 1:55 am
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
OA B

If you know a simple method to determine this, please share.

Thanks
Top
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 1893
Joined: Sun May 30, 2010 11:48 pm
Thanked: 215 times
Followed by:7 members

by kvcpk » Sun Aug 01, 2010 2:57 am
MFSD1D2
driver seat can be filled in 2 ways.

Assume Pillion seat is filled by the other parent. this can be done in 1 way
Then, back seats can be filled in only 2 ways (D1SD2 or D2SD1) so that the daughters dont sit together.
All three should happen together. Hence 2*1*2= 4 ways.

Assume Pillion seat is filled by the son. this can be done in 1 way
Then, back seats can be filled in only 2 ways (D1MD2 or D2MD1) so that the daughters dont sit together.
All three should happen together. Hence 2*1*2 = 4 ways.

Assume Pillion seat is filled by the daughter. this can be done in 2 ways.
Then, back seats can be filled in only 3! = 6 ways because there is no restriction.
All three should happen together. Hence 2*2*6 = 24 ways.

Any of these should occur. Hence Add. 4+4+24 = 32 ways.

Hope this helps!!
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 362
Joined: Fri Oct 02, 2009 4:18 am
Thanked: 26 times
Followed by:1 members

by indiantiger » Sun Aug 01, 2010 1:44 pm
D-------P

R1 R2 R3

D - driver seat
P - passenger seat
R1 = rear 1
R2 = rear 2
R3 = rear 3

Case 1 :

D can be filled in 2 ways with either parent
P can be filled in 2 ways with either parent not driving or son
R1 can be filled in 2 ways by either sister
R2 has to filled by who ever did not get to sit on P (either son or parent) 1 way
R3 can be filled by left out sister.

total ways in this case = 8

Case 2
D can be filled in 2 ways with either parent
P can be filled in 2 ways with either sister
R1 can be filled in 3 ways by sister who did not get the P seat, son or parent who is not driving
R2 has to filled 2 ways by (sister who did not get the P seat, son or parent who is not driving) -1 as one of these must have sat on R1
R3 can be filled by left out person
total ways in this case = 24

Total overall cases = 24+8 = 32.
"Single Malt is better than Blended"
Top
Post new topic Post Reply
• Page 1 of 1