continents arrangements

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

continents arrangements

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...

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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 pm; Thanked: 331 times; Followed by:11 members

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.

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

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.

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

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

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

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.

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

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

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logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pm; Thanked: 237 times; Followed by:25 members; 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.

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

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