Find all School-related info fast with the new School-Specific MBA Forum

It is currently 19 Sep 2014, 12:06

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Amy and Adam are making boxes of truffles to give out as wed

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Senior Manager
Senior Manager
avatar
Joined: 11 Apr 2011
Posts: 268
Followers: 27

Kudos [?]: 222 [0], given: 13

GMAT ToolKit User
Amy and Adam are making boxes of truffles to give out as wed [#permalink] New post 20 Jun 2011, 19:16
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

80% (01:41) correct 20% (00:43) wrong based on 1 sessions
Amy and Adam are making boxes of truffles to give out as wedding favors. They have an unlimited supply of 5 different types of truffles. If each box holds 2 truffles of different types, how many different boxes can they make?

I understand these are all the possible combinations:

Box 1: A B
Box 2: A C
Box 3: A D
Box 4: A E
Box 5: B C
Box 6: B D
Box 7: B E
Box 8: C D
Box 9: C E
Box 10: D E

But I don't get the mathematical interpretation of this.. 5! / (3! * 2!)

I don't get how the anagram can be "YYNNN"
_________________

Powerscore CR Bible Full Chapter Notes | Easily Extend Vocabulary List with Google Dictionary

Please kudo me if you found my post useful. Thanks!!! :)

Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4777
Location: Pune, India
Followers: 1116

Kudos [?]: 5066 [0], given: 164

Re: MGMAT Word Translations COMBINATORICS!!! [#permalink] New post 21 Jun 2011, 01:39
Expert's post
Mahtab wrote:
Amy and Adam are making boxes of truffles to give out as wedding favors. They have an unlimited supply of 5 different types of truffles. If each box holds 2 truffles of different types, how many different boxes can they make?

I understand these are all the possible combinations:

Box 1: A B
Box 2: A C
Box 3: A D
Box 4: A E
Box 5: B C
Box 6: B D
Box 7: B E
Box 8: C D
Box 9: C E
Box 10: D E

But I don't get the mathematical interpretation of this.. 5! / (3! * 2!)

I don't get how the anagram can be "YYNNN"


You can think of it in 2 ways:
1. You have 5 different types of truffles. For each box, you have to select 2 different types of truffles. In how many ways can you do it?
5C2 = 5!/3!*2!
(When out of n things, you have to select r, you can do it in nCr ways. nCr = n!/r!*(n-r)!
For more on this, check out Combinatorics & Probability by Veritas Prep)
2. There are 5 truffles. You need to select 2 and not select the rest of the three. Y - select a truffle. N - Do not select it
So you can select 2 truffles in the number of ways in which you can arrange YYNNN.
YYNNN means you select the first 2 and leave the rest.
YNYNN means you select 1st and 3rd and leave the rest.
etc...
This can be done in 5!/2!*3!
You can arrange 5 things in 5! ways. But you have 2 Ys and 3 Ns so you divide by 2! and 3!.
(Again, for more on this, check out Combinatorics & Probability by Veritas Prep)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Senior Manager
Senior Manager
avatar
Joined: 11 Apr 2011
Posts: 268
Followers: 27

Kudos [?]: 222 [0], given: 13

GMAT ToolKit User
Re: MGMAT Word Translations COMBINATORICS!!! [#permalink] New post 21 Jun 2011, 04:37
Yeah I was doing so well in Quant up until I hit Guide 4 of MGMAT Combinatorics...they did an adaquete job at explaining it so I bought the Veritas Combinatorics book from amazon last night! I will put this to rest for a few days I guess and move on to statistics.

Thanks and I kind of understand the nCr thing but I want to go more in depth of the concept so I have a strong foundation.

Thanks!
_________________

Powerscore CR Bible Full Chapter Notes | Easily Extend Vocabulary List with Google Dictionary

Please kudo me if you found my post useful. Thanks!!! :)

Intern
Intern
avatar
Joined: 16 Jun 2011
Posts: 33
Followers: 0

Kudos [?]: 1 [0], given: 6

Re: MGMAT Word Translations COMBINATORICS!!! [#permalink] New post 21 Jun 2011, 13:34
Project GMAT - also Veritas covers these fairly well, also
Intern
Intern
avatar
Joined: 14 Jan 2013
Posts: 25
Location: India
Followers: 0

Kudos [?]: 6 [0], given: 43

GMAT ToolKit User
Re: Amy and Adam are making boxes of truffles to give out as wed [#permalink] New post 20 Jul 2013, 10:49
Hi, I have an issue with comprehending such problems. Could any of you correct me please. I know the solution to the problem is 10.

My approach is : Each box can contain two truffles, so if I say there are two slots in the box then the first slot has the possibility of 5 different types of truffles and the next slot has the possibility of 4 different types of truffles. So i concluded 5*4 = 20 as the answer.

Can any of you please identify the flaw in my approach to the problem. Again, I know the solution, but I want to know what exactly is the flaw in the argument presented above, so that I don't repeat the mistake again.
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23482
Followers: 3501

Kudos [?]: 26448 [1] , given: 2712

Re: Amy and Adam are making boxes of truffles to give out as wed [#permalink] New post 20 Jul 2013, 11:14
1
This post received
KUDOS
Expert's post
kiranck007 wrote:
Hi, I have an issue with comprehending such problems. Could any of you correct me please. I know the solution to the problem is 10.

My approach is : Each box can contain two truffles, so if I say there are two slots in the box then the first slot has the possibility of 5 different types of truffles and the next slot has the possibility of 4 different types of truffles. So i concluded 5*4 = 20 as the answer.

Can any of you please identify the flaw in my approach to the problem. Again, I know the solution, but I want to know what exactly is the flaw in the argument presented above, so that I don't repeat the mistake again.


The problem with your solution is that 20 has duplications in it: box holding {A, B} is the same as the box holding {B, A} and 5*4 will give you both boxes.

The question basically asks: in how many ways we can select 2 different truffles out of 5, which is simply C^2_5=10.

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

1 KUDOS received
VP
VP
User avatar
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1125
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Followers: 112

Kudos [?]: 1152 [1] , given: 219

GMAT ToolKit User GMAT Tests User
Re: Amy and Adam are making boxes of truffles to give out as wed [#permalink] New post 20 Jul 2013, 11:17
1
This post received
KUDOS
kiranck007 wrote:
Hi, I have an issue with comprehending such problems. Could any of you correct me please. I know the solution to the problem is 10.

My approach is : Each box can contain two truffles, so if I say there are two slots in the box then the first slot has the possibility of 5 different types of truffles and the next slot has the possibility of 4 different types of truffles. So i concluded 5*4 = 20 as the answer.

Can any of you please identify the flaw in my approach to the problem. Again, I know the solution, but I want to know what exactly is the flaw in the argument presented above, so that I don't repeat the mistake again.


I think you are using the slot-method. I am not very familiar with it, but you are missing the last step:

_ _ , two slots that can be filled in 5*4=20 ways. Correct till here, but then you have to divide for the "factorial" number of interchangeable slots, in this case 2!=2. So the final result is \frac{5*4}{2}=10.
_________________

It is beyond a doubt that all our knowledge that begins with experience.

Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]

Manager
Manager
avatar
Joined: 27 Aug 2009
Posts: 51
Followers: 0

Kudos [?]: 2 [0], given: 1

Re: Amy and Adam are making boxes of truffles to give out as wed [#permalink] New post 09 Jul 2014, 14:21
Can someone explain the differences in the approaches you would take if you could pick 2 of the same type of truffle vs how in this problem you can only use one type of each truffle per box?

I understand with the anagram method the latter is YYNNN - out of five choices, two of those five will be picked and three of those 5 will not be picked, therefore the answer is 5!/2!3!

But what about if dupes were allowed, how would the calculation change? Obviously that's a pretty easy thing to manually add but I'd like to understand the process.
Re: Amy and Adam are making boxes of truffles to give out as wed   [#permalink] 09 Jul 2014, 14:21
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic In a department store prize box, 40% of the notes give... jlgdr 1 18 Sep 2013, 11:31
1 Some Out of the Box FORMULAS and SHORTCUTS m2l2 0 13 May 2011, 08:27
Amy and Adam are making boxes of truffles to give out as amitdgr 4 28 Sep 2008, 05:50
I am giving the GMAT on Nov 21st, Wed gluon 3 19 Nov 2007, 11:55
6 What do you make out of this ? rgajare14 8 30 Sep 2007, 11:34
Display posts from previous: Sort by

Amy and Adam are making boxes of truffles to give out as wed

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.