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

Redeem

along with group :( - permutation / combination prob

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 423
Joined: Fri Jun 11, 2010 7:59 am
Location: Seattle, WA
Thanked: 86 times
Followed by:2 members

by srcc25anu » Sun Mar 20, 2011 1:21 am
lets count each couple as 1 so there are total of 6 people (each couple counted as 1 each)
6 people can sit in 6! ways
now each couple can sit in 2 ways * 2 ways
total ways = 6!*2*2 = 2880
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 436
Joined: Tue Feb 08, 2011 3:07 am
Thanked: 72 times
Followed by:6 members

by manpsingh87 » Sun Mar 20, 2011 5:58 am
AIM GMAT wrote:A group of 8 students take up a full row at a movie theater. There are 2 couples and the
2 people within each couple must sit together. In how many di& erent arrangements can
the students sit?
let c1 represents couple 1, and c2 represents couple 2, and the remaining four students be represented as s1,s2,s3,s4. Also let people within c1 and c2 be p1,p2,p3,p4 respectively.

as two persons within each couple must sit together therefore people within c1 and c2 will be consider as 1, so therefore we have total of 6 objects. these six objects can arrange themselves in 6! ways.

c1[(p1,p2)],c2[(p3,p4)],s1,s2,s3,s4 {it is one of the way of arrangement.}

now p1,p2 can interchange their position within a group in 2! ways similarly for p3 and p4 we have 2! ways.

so total no. of ways of arrangements would be 6!*2!*2!=2880
O Excellence... my search for you is on... you can be far.. but not beyond my reach!
Top
User avatar
Legendary Member
Posts: 582
Joined: Tue Mar 08, 2011 12:48 am
Thanked: 61 times
Followed by:6 members
GMAT Score:740

by force5 » Sun Mar 20, 2011 9:42 am
Total ways = 6!*2!*2! = 2880
Top
Senior | Next Rank: 100 Posts
Posts: 56
Joined: Sat Dec 11, 2010 2:39 pm
Thanked: 3 times

by gmat7202011 » Sun Mar 20, 2011 6:59 pm
Since the 2 couples must sit together, consider them as 1 person to start with, so there are 6 students, which can sit in
6! ways,

Now there were 2 couples, which we substituted as 1 student each to find the unique ways, get them back
6! x 2! x 2!

Is this the correct answer ?

Thank You,
Top
Legendary Member
Posts: 857
Joined: Wed Aug 25, 2010 1:36 am
Thanked: 56 times
Followed by:15 members

by AIM GMAT » Sun Mar 20, 2011 11:06 pm
Yep guys you all are correct , the answer is 2880.
Thanks & Regards,
AIM GMAT
Top
Post new topic Post Reply
• Page 1 of 1