continents arrangements

Expert replies

cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Sat Mar 07, 2009 4:58 pm

Six students form 3 pairs and they have to be assigned to 3 different continents. How many ways can they be assigned?

Dont have an OA, sorry.

Interested in the approaches and we will get to an OA, hopefully...

Like this post

Source: Beat The GMAT — Problem Solving | Sat Mar 07, 2009 4:58 pm

cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Sat Mar 07, 2009 5:07 pm

A B C D E F
There can be only 15 unique pairs from 6 different people and the order does not matter in the pair since its like picking a commitee.

3 pairs can be picked from 15 pairs in 15c3 ways.

Then these 3 pairs can be arranged in 3! i.e 6 ways in the continents

6*15c3 = 2730

Stuart/Ian or others please feel free to share your thoughts.

My question is if:

AB is assigned to continent 1
CD to continent 2
EF to continent 3

AND

AB is assigned to continent 1
DF assigned to continent 2
CE assigned to continent 3

considered as 2 different ways. I think so and hence my 2730 answer. Please correct me if I am mistaken.

Last edited by cramya on Sun Mar 08, 2009 9:40 am, edited 2 times in total.

Like this post

mals24: Legendary Member; Posts: 683; Joined: Tue Jul 22, 2008 1:58 pmFollowed by: 2 members; Location: Dubai; Thanked: 73 times

by mals24 » Sun Mar 08, 2009 3:33 am

Firstly,

Dont have an OA, sorry.

Secondly,

AB is assigned to continent 1
BD assigned to continent 2
CE assigned to continent 3

I have a question. If B is in continent 1 how can B be in continent 2 at the same time. So, according to me, we cannot have a combination of AB and BD at the same time.

Thirdly, my solution

A B C D E F

Number of groups that can be formed from 6 people: 6C2 = 15
Number of ways of assigning 15 groups.

Continent 1: We have 15 ways of selecting 1 group for this continent (15C1)

Continent 2: For instance, if we selected pair AB for Cont 1, we can choose our next group from the remaining 4 people (C D E F). So number of ways of selecting 2 people from 4 = 4C2 = 6

Continent 3: For this continent we'll have only 2 people remaining so just one group.

So total number of ways of arranging 15 groups into 3 continents = 15*6*1 = 90

Just my opinion.

Like this post

Vemuri: Legendary Member; Posts: 682; Joined: Fri Jan 16, 2009 2:40 amFollowed by: 1 member; Thanked: 32 times

Re: continents arrangements

by Vemuri » Sun Mar 08, 2009 5:48 am

I am not good with Permutations, Combinations & Probability. But, will give my shot at this question

3 pairs can be formed using 6 students in 20 ways (6c3). The 3 pairs can be assigned to 3 different continents in 6 ways (3!). So, adding 20+6=26ways is my answer.

I hope I am correct

Like this post

cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Sun Mar 08, 2009 9:39 am

Thanks Mals and Vemuri for attempting it.

I have a question. If B is in continent 1 how can B be in continent 2 at the same time. So, according to me, we cannot have a combination of AB and BD at the same time.

Mals, sorry that was a typo and have corrected it.

Like this post

cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Sun Mar 08, 2009 10:07 am

Mals, I think u may be right. Good solution.

Hoping Ian/Stuart can confirm this also.

Regards,
Cramya

Like this post

logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pmFollowed by: 25 members; Thanked: 237 times; GMAT Score:730

by logitech » Sun Mar 08, 2009 2:03 pm

Okay, let's learn some concepts by playing with them:

WHAT IF,

if we decide that continents are not moving anywhere

1 2 3

and we will assign people to them:

AB CD EF

so they can be listed as 3!= 6 ways

how many different pairs can we get ? 6C2= 15

so 15x6=90

Do you agree with this logic ? If not, why ?

Last edited by logitech on Sun Mar 08, 2009 2:07 pm, edited 1 time in total.

LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"

Like this post

GMAT/MBA Expert

Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Mon Mar 09, 2009 6:48 am

I don't like the wording of the original question, which could be interpreted in different ways, but as I read it, I agree with Logitech's solution above. Really, you're just selecting three teams of two from six people, and putting them in order. So, if we start by selecting a pair for 'Europe', we have 6C2 = 15 choices. We then select a second pair for 'Asia' and we have 4C2 = 6 choices. Finally, the remaining pair must be assigned to 'South America', or whatever continent we're using. We multiply our choices when we're assigning things to positions, so we should have 15*6 = 90 assignments in total.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

Like this post

cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Mon Mar 09, 2009 2:12 pm

Thanks Ian,Logitech, Mals and Vemuri.

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review