NEW HERE? LEARN MORE
closeclose
Last visit was: 27 Apr 2024, 07:24 It is currently 27 Apr 2024, 07:24
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

A family consisting of one mother, one father, two daughters

SORT BY:
Date
Kudos
   1   2 
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
B
ashdank94
Intern
Intern
Joined: 20 Feb 2023
Posts: 31
Own Kudos [?]: 6 [1]
Given Kudos: 100
Send PM
Re: A family consisting of one mother, one father, two daughters [#permalink] New post   27 Mar 2024, 12:22
MartyMurray Wondering if my method makes sense:

Father or Mother drives: 2!
The remaining 4 seats can be arranged in the following ways: 4! - 2!(4-2+1)! = 4! - 2!3!

Total = 2! x (4! - 2!3!)

Could you let me know what I did wrong here?
User avatar
P
MartyMurray
Tutor
Joined: 11 Aug 2023
Posts: 826
Own Kudos [?]: 1420 [0]
Given Kudos: 75
GMAT 1: 800 Q51 V51
Send PM
Re: A family consisting of one mother, one father, two daughters [#permalink] New post   28 Mar 2024, 11:11
Expert Reply
ashdank94 wrote:
MartyMurray Wondering if my method makes sense:

Father or Mother drives: 2!
The remaining 4 seats can be arranged in the following ways: 4! - 2!(4-2+1)! = 4! - 2!3!

Total = 2! x (4! - 2!3!)

Could you let me know what I did wrong here?

­Where did you get this? 2!(4-2+1)!

It should be

the two daughters can sit next to each other in two ways: 2

the daughters next to each other can be on the right or the left: 2

the third person in the back can be a parent or the son: 2

So, 2!2!2!.
User avatar
B
ashdank94
Intern
Intern
Joined: 20 Feb 2023
Posts: 31
Own Kudos [?]: 6 [0]
Given Kudos: 100
Send PM
Re: A family consisting of one mother, one father, two daughters [#permalink] New post   28 Mar 2024, 11:17
MartyMurray I used the method from TTP.

If the 2 daughters cannot be together I arrange them as 4! - 2!(4-2+1)!

arrange the daughters together, and multiply ways by which the others can be arranged and subtract from 4!

Is this method application wrong?

Posted from my mobile device
User avatar
P
MartyMurray
Tutor
Joined: 11 Aug 2023
Posts: 826
Own Kudos [?]: 1420 [0]
Given Kudos: 75
GMAT 1: 800 Q51 V51
Send PM
Re: A family consisting of one mother, one father, two daughters [#permalink] New post   28 Mar 2024, 11:41
Expert Reply
 
ashdank94 wrote:
MartyMurray I used the method from TTP.

If the 2 daughters cannot be together I arrange them as 4! - 2!(4-2+1)!

arrange the daughters together, and multiply ways by which the others can be arranged and subtract from 4!

Is this method application wrong?

Posted from my mobile device

Oh, I think I get it.

I think the issue is that you didn't keep in mind that the two daughers together can be in the back only. So, there are only two positions for the two daugthers together, on the right or the left in the back seats.

So, you can't apply the method normally. You have to take the additional constraint into account.

With that constraint taken into account, the ways the 4 passengers can be arranged is 4! - the arrangements with daugters next to each other.

4! - (2 × 2 × 2) = 24 - 8 =16
User avatar
B
ashdank94
Intern
Intern
Joined: 20 Feb 2023
Posts: 31
Own Kudos [?]: 6 [0]
Given Kudos: 100
Send PM
Re: A family consisting of one mother, one father, two daughters [#permalink] New post   28 Mar 2024, 11:45
Interesting :) it wasn’t specified in the question that daughters have to sit in the back so I assumed it was a shotgun situation lol

Posted from my mobile device
User avatar
P
MartyMurray
Tutor
Joined: 11 Aug 2023
Posts: 826
Own Kudos [?]: 1420 [0]
Given Kudos: 75
GMAT 1: 800 Q51 V51
Send PM
Re: A family consisting of one mother, one father, two daughters [#permalink] New post   28 Mar 2024, 11:48
Expert Reply
ashdank94 wrote:
Interesting :) it wasn’t specified in the question that daughters have to sit in the back so I assumed it was a shotgun situation lol

­Haha. Yeah, the idea is that they can't sit "next to each other" in one front seat.
User avatar
B
Prince1890Sharma
Intern
Intern
Joined: 19 Mar 2023
Posts: 19
Own Kudos [?]: 8 [0]
Given Kudos: 33
Send PM
CAT Tests
Re: A family consisting of one mother, one father, two daughters [#permalink] New post   06 Apr 2024, 22:14
Hello Bunuel,

Is this way of solving correct

Posted from my mobile device
Attachments

17124668236712497605722482596011.jpg
17124668236712497605722482596011.jpg [ 419.83 KiB | Viewed 185 times ]

User avatar
B
Contropositive
Intern
Intern
Joined: 21 Oct 2023
Posts: 28
Own Kudos [?]: 3 [0]
Given Kudos: 16
Location: India
Send PM
Re: A family consisting of one mother, one father, two daughters [#permalink] New post   10 Apr 2024, 23:45
 
KarishmaB wrote:
Engineer1 wrote:
pratikbais wrote:
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

MartyMurray KarishmaB let me know if this looks correct.

Taking all mother as driver scenarios. For father as driver scenarios, both will be multiplied by 2.

Scenario 1:
M F
D1 S D2

For D1, D2 arrangement in the back seats (2)
For F, S arrangement between back and front seats (2)
So, 2 * 2 = 4

Multiplying by 2 again, to consider father. Therefore this gives me 8.

Scenario 2:
M D1
D2 S F

For D1, D2 front and back seat exchange (2)
For F and S seating arrangement in the backseats (2)
A D1 or D2 can be seated in the backseats is (3) ways
So, 2 * 2 * 3 = 12

Multiplying by 2 again, to consider father. Therefore this gives me 24.

Adding both scenarios above = 24+8 = 32 (B)

Looks fine though I would worry if I missed some cases in solving it this way. I would much rather go the 'All - NOT Allowed' way.

I pick a driver in 2 ways.

All other 4 people can be arranged in 4! ways.

Not Allowed Cases - Make the daughters sit together (make a group) in the back seat. Pick one more person for the backseat (out of father and son) in 2 ways.
Now arrange the group and the third person in 2! * 2! (arrangement of the two daughters)
Total arrangements = 2 * 2 * 2 = 8

Hence Allowed arrangements = 2 * (4! - 8) = 32

Answer (B)

Check out this video on Permutations:


­Hi KarishmaB
Bunuel
In the total number of cases, why haven't we considered that drivers seat can be either on the RIGHT side or LEFT side?

TOTAL CASES
If Driver's seat was on right side:

Number of ways to choose driver = 2
Rest people can sit in 4! ways

Same will be the case with left side. 
Hence, total number of cases will be = 2 x 2 x 4! = 96

Now, number of cases wherein ''Daughters'' are together:

If Driver's seat is on Right end:
Number of ways to choose driver = 2
number of ways daughers sit = 4: (_, D1, D2), (_ D2, D1), (D1, D2, _), (D2, D1, _) 
number of ways, rest people sit: 2

Total cases on Right = 16
Same will on the left side 

Total cases with consecutuve daughters = 32

Remaining cases = 96-32 = 64­
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92952
Own Kudos [?]: 619388 [0]
Given Kudos: 81611
Send PM
CAT Tests Forum Quiz Mode
Re: A family consisting of one mother, one father, two daughters [#permalink] New post   10 Apr 2024, 23:56
Expert Reply
Contropositive wrote:
­Hi KarishmaB
Bunuel
In the total number of cases, why haven't we considered that drivers seat can be either on the RIGHT side or LEFT side?

TOTAL CASES
If Driver's seat was on right side:

Number of ways to choose driver = 2
Rest people can sit in 4! ways

Same will be the case with left side. 
Hence, total number of cases will be = 2 x 2 x 4! = 96

Now, number of cases wherein ''Daughters'' are together:

If Driver's seat is on Right end:
Number of ways to choose driver = 2
number of ways daughers sit = 4: (_, D1, D2), (_ D2, D1), (D1, D2, _), (D2, D1, _) 
number of ways, rest people sit: 2

Total cases on Right = 16
Same will on the left side 

Total cases with consecutuve daughters = 32

Remaining cases = 96-32 = 64­

­
The driver's seat is where the steering wheel is located and cannot be moved from one side to the other.

­
GMAT Club Bot
gmatclubot
Re: A family consisting of one mother, one father, two daughters [#permalink]
10 Apr 2024, 23:56
   1   2 
Moderators:
Bunuel
Math Expert
92952 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions