It is currently 18 Oct 2017, 11:45

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

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

Hide Tags

Senior Manager
Joined: 11 Apr 2011
Posts: 264

Kudos [?]: 659 [0], given: 13

Amy and Adam are making boxes of truffles to give out as wed [#permalink]

Show Tags

20 Jun 2011, 20:16
00:00

Difficulty:

(N/A)

Question Stats:

80% (00:41) correct 20% (00:43) wrong based on 1 sessions

HideShow timer Statistics

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!!!

Kudos [?]: 659 [0], given: 13

Math Expert
Joined: 02 Sep 2009
Posts: 41888

Kudos [?]: 128750 [1], given: 12182

Re: Amy and Adam are making boxes of truffles to give out as wed [#permalink]

Show Tags

20 Jul 2013, 12:14
1
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.
_________________

Kudos [?]: 128750 [1], given: 12182

VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1120

Kudos [?]: 2327 [1], given: 219

Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Re: Amy and Adam are making boxes of truffles to give out as wed [#permalink]

Show Tags

20 Jul 2013, 12:17
1
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]

Kudos [?]: 2327 [1], given: 219

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7674

Kudos [?]: 17349 [0], given: 232

Location: Pune, India
Re: MGMAT Word Translations COMBINATORICS!!! [#permalink]

Show Tags

21 Jun 2011, 02:39
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

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Kudos [?]: 17349 [0], given: 232

Senior Manager
Joined: 11 Apr 2011
Posts: 264

Kudos [?]: 659 [0], given: 13

Re: MGMAT Word Translations COMBINATORICS!!! [#permalink]

Show Tags

21 Jun 2011, 05:37
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!!!

Kudos [?]: 659 [0], given: 13

Intern
Joined: 16 Jun 2011
Posts: 32

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

Re: MGMAT Word Translations COMBINATORICS!!! [#permalink]

Show Tags

21 Jun 2011, 14:34
Project GMAT - also Veritas covers these fairly well, also

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

Intern
Joined: 14 Jan 2013
Posts: 23

Kudos [?]: 12 [0], given: 43

Location: India
Re: Amy and Adam are making boxes of truffles to give out as wed [#permalink]

Show Tags

20 Jul 2013, 11:49
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.

Kudos [?]: 12 [0], given: 43

Current Student
Joined: 27 Aug 2009
Posts: 51

Kudos [?]: 4 [0], given: 1

Schools: Fuqua (A)
Re: Amy and Adam are making boxes of truffles to give out as wed [#permalink]

Show Tags

09 Jul 2014, 15:21
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.

Kudos [?]: 4 [0], given: 1

Re: Amy and Adam are making boxes of truffles to give out as wed   [#permalink] 09 Jul 2014, 15:21
Display posts from previous: Sort by