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

It is currently 22 Jul 2014, 14:10

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

At a blind taste competition a contestant is offered 3 cups

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18683
Followers: 3232

Kudos [?]: 22197 [0], given: 2601

Re: At a blind taste competition a contestant is offered 3 cups [#permalink] New post 06 Mar 2013, 01:32
Expert's post
tosattam wrote:
Not sure if my channel of thought is flawed to start with, but when it is said that it's a 'blind' taste competition, I am considering repetitions. As the contestant does not know which of the 9 cups he/she had picked up the first time, the same can possibly be repeated in the second turn and so on until the fourth.
That gives a complete different perspective to the problem.
Where am I going wrong here?


A blind taste simply means that a contestant doesn't know which samples he/she is offered to taste.

_________________

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

Intern
Intern
avatar
Joined: 22 Dec 2012
Posts: 16
GMAT 1: 720 Q49 V39
Followers: 1

Kudos [?]: 9 [0], given: 19

Re: Diagnostic Question [#permalink] New post 09 Mar 2013, 21:37
Hi,
Let me try..
mainhoon, you are going with the logic that you select 1 cup from each sample in 3c1 x 3c1 x 3c1 ways and 1 remaining cup from 6 cups in 6c1 ways rite!
I guess the flaw with your approach is that this 6c1 is the probablity of selecting 1 item from 6 DIFFERENT items (r items from n different items is nCr)
Im this case the 6 items left are not different! They are XX,YY,ZZ types right! so you just cant use the 6c1 fomula!
This is the formula : The number of ways of choosing r objects from p objects of one kind, q objects of second kind, and so on is the coefficient of x^r in the expansion
Image

hope it helps!



mainhoon wrote:
Yes I can see that clearly I am ending up with more combinations than necessary. I was thinking if there is way to factor out those repeats the way I am doing it. I see your point in the simple example. However when I think of this, I am thinking of a 3x3 matrix where I have to make sure I get one from each row and the 4th can come from anywhere - that is the same thing as saying 2 from a row and 1 each from the remaining 2 (your and correct approach). My count differs from yours by a factor of 2 (I am 162 and you are 81). How can I rationalize this?
Intern
Intern
avatar
Joined: 10 Dec 2013
Posts: 19
Location: India
Concentration: Technology, Strategy
GMAT 1: 710 Q48 V38
GPA: 3.9
WE: Consulting (Consulting)
Followers: 0

Kudos [?]: 6 [0], given: 7

Re: At a blind taste competition a contestant is offered 3 cups [#permalink] New post 29 Jan 2014, 10:59
If we employ the counting method applied in the question http://gmatclub.com/forum/tough-p-n-c-92675.html then
Considering three different samples and contestant not to taste all three samples there would be following two conditions

1. Contestant tastes 3 cups of on sample and 1 cup of another
i.e. AAAB
The number of ways this can happen is
3C2*4!/3! = 12
3C2 = Ways to select any 2 samples out of the 3 choices
4!/3! = # of ways AAAB can be rearranged

or
2. Contestant tastes 2 cups of a sample and 2 of another
i.e. AABB
The number of ways this could happen is
3C2*4!/(2!*2!) = 18
3C2 = Ways to select any 2 samples out of the 3 choices
4!/(2!*2!) = # of ways AABB can be rearranged

Hence total number of ways by which contestant can only taste any two samples is 18 + 12 = 30

Total number of ways to select 4 cups from 9 = 9C4 = 126

hence the probability that contestant can only taste any two samples = 30/126
= 5/21

Is this approach not correct? Where am I missing ?
Manager
Manager
User avatar
Joined: 11 Jan 2014
Posts: 95
Concentration: Finance, Statistics
GMAT Date: 03-04-2014
GPA: 3.77
WE: Analyst (Retail Banking)
Followers: 2

Kudos [?]: 31 [0], given: 7

Re: At a blind taste competition a contestant is offered 3 cups [#permalink] New post 29 Jan 2014, 11:22
Great explanations above. A rather headache-inducing question, I admit I had to resolve to the following guessing pattern after I passed the 1:36 mark and admitted defeat. :lol:

Economist wrote:
At a blind taste competition a contestant is offered 3 cups of each of the 3 samples of tea in a random arrangement of 9 marked cups. If each contestant tastes 4 different cups of tea, what is the probability that a contestant does not taste all of the samples?

A. \frac{1}{12} Too low
B. \frac{5}{14} Looks reasonable
C. \frac{4}{9} Impossible, cannot be that simple
D. \frac{1}{2} Too high
E. \frac{2}{3} Too high
Intern
Intern
avatar
Joined: 10 Dec 2013
Posts: 19
Location: India
Concentration: Technology, Strategy
GMAT 1: 710 Q48 V38
GPA: 3.9
WE: Consulting (Consulting)
Followers: 0

Kudos [?]: 6 [0], given: 7

Re: At a blind taste competition a contestant is offered 3 cups [#permalink] New post 30 Jan 2014, 01:50
Quote:
If we employ the counting method applied in the question tough-p-n-c-92675.html then
Considering three different samples and contestant not to taste all three samples there would be following two conditions

1. Contestant tastes 3 cups of on sample and 1 cup of another
i.e. AAAB
The number of ways this can happen is
3C2*4!/3! = 12
3C2 = Ways to select any 2 samples out of the 3 choices
4!/3! = # of ways AAAB can be rearranged

or
2. Contestant tastes 2 cups of a sample and 2 of another
i.e. AABB
The number of ways this could happen is
3C2*4!/(2!*2!) = 18
3C2 = Ways to select any 2 samples out of the 3 choices
4!/(2!*2!) = # of ways AABB can be rearranged

Hence total number of ways by which contestant can only taste any two samples is 18 + 12 = 30

Total number of ways to select 4 cups from 9 = 9C4 = 126

hence the probability that contestant can only taste any two samples = 30/126
= 5/21

Is this approach not correct? Where am I missing ?



I have come up with another approach which gives a different result again.

Assuming the that the contestant does not taste the 3rd sample there are 2 scenarios possible

AABB and AAAB

Counting one at a time.
#of ways AABB can occur = 3C2*3C2*3C2 = 27
here,
3C2 = ways to select the 2 samples from 3
3C2 = ways to select the 2 cups from 3 cups of first sample
3C2 = ways to select 2 cups from 3 cups of second sample

# of ways AAAB can occur = 3C2*3C3*3C1 = 9
3C2 = ways to select the 2 samples from 3
3C3 = ways to select 3 cups from the 3 cups of first sample
3C1 = ways to select 1 cup from the 3 cups of second sample

Hence the total number of ways in which the contestant cannot taste any cup from third sample = 9 +27 = 36

Total number of ways to select 4 cups from 9 = 9C4 = 126

hence the probability that contestant can only taste any two samples = 36/126
= 4/14

Even after hours and hours of going through various material on Probablity and combinations I am struggling to identify a uniform approach that can be applied across problems. How would one know which approach to apply for which problem during the exams. Is there any way we can determine that? :(
Re: At a blind taste competition a contestant is offered 3 cups   [#permalink] 30 Jan 2014, 01:50
    Similar topics Author Replies Last post
Similar
Topics:
1 Experts publish their posts in the topic Premium Membership Contest Verbal Q3 souvik101990 11 21 Apr 2014, 08:59
Experts publish their posts in the topic A recipe requires 2 1/2 cups of flour 2 3/4 cups of sugar clciotola 6 17 May 2013, 07:03
Chances of Getting into a need blind university with 3.03GPA bvishwajit 2 25 Jul 2011, 01:34
Experts publish their posts in the topic Competition mohitguptask 2 07 Nov 2004, 10:53
There are 5 contestants, A, B, C, D, E contesting for 3 cbrf3 3 10 Aug 2004, 04:54
Display posts from previous: Sort by

At a blind taste competition a contestant is offered 3 cups

  Question banks Downloads My Bookmarks Reviews Important topics  

Go to page   Previous    1   2   [ 25 posts ] 



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®.