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

Redeem

combinatrics

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Master | Next Rank: 500 Posts
Posts: 232
Joined: Fri Jun 18, 2010 7:09 am
Thanked: 1 times
Followed by:2 members

combinatrics

by ruplun » Mon Aug 01, 2011 11:34 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?
Top
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 370
Joined: Sat Jun 11, 2011 8:50 pm
Location: Arlington, MA.
Thanked: 27 times
Followed by:2 members

by winniethepooh » Mon Aug 01, 2011 12:19 pm
We can calculate this by finding the number of ways the family can sit without any restrictions and then deducting the number of ways the daughters can sit together(only)

Clculating the number of ways w/0 restrictions:
2 ways for front driver seat
4 ways for the front passenger seat
3 ways for left back seat
2 ways for mibble back seat and
1 way for the left back seat
= 2*4*3*2*1 = 48 ways.

Calculating the number of ways the daughter can sit together.
They can sit together only in the back seat:Hence, the daughters will only be placed at the back.
2 ways for front driver seat
2 ways for front passenger seat(the son or one of the parents)
2 ways for the back seats.(2 daughter sit together so they can be considered 1 unit and the remaining of son or any parent)
1 way for the remaining(Either 2 daughter or son or any parent.
total ways = 2*2*2*1 = 8 ways.
but you have to multiply this number by 2 (the number of ways the daughters can arrange amongst themselves.
So, total number of ways = 2*8 = 16 ways.
The number of ways with restrictions = 48-16 = 32ways.
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Mon Aug 01, 2011 2:24 pm
I posted a solution here:

https://www.beatthegmat.com/difficult-pr ... 87921.html
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Post new topic Post Reply
• Page 1 of 1