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

It is currently 24 Oct 2014, 22:48

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

There are five flavors of icecream: banana, chocolate, lemon

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 24 Sep 2009
Posts: 23
Followers: 4

Kudos [?]: 69 [0], given: 2

There are five flavors of icecream: banana, chocolate, lemon [#permalink] New post 24 Sep 2009, 19:06
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

100% (01:36) correct 0% (00:00) wrong based on 1 sessions
There are five flavors of icecream: banana, chocolate, lemon, strawberry and vanilla. You can have three scoops. How many variations will there be?

[Reveal] Spoiler:
Why is the answer 35 = 7!/(3!x4!) and not 5^3 written like (5*5*5)=125?

Thank you
Intern
Intern
avatar
Joined: 13 Sep 2009
Posts: 16
Followers: 0

Kudos [?]: 3 [0], given: 0

Re: Permutation / combinations [#permalink] New post 24 Sep 2009, 21:56
benjiboo wrote:
There are five flavors of icecream: banana, chocolate, lemon, strawberry and vanilla. You can have three scoops. How many variations will there be?






Why is the answer 35 (7!/3!x4!) and not 5^3 written like (5*5*5)=125?

Thank you


It is combination case, isn't it? but I got 25 ways instead of 35, my process to come to this result as follow, not sure where is it went wrong.
B C L S V
3 0 0 0 0 -->C(5,1)= 5 ways
2 1 0 0 0 -->C(5,2)=10 ways
1 1 1 0 0 -->C(5,3)=10 ways
Senior Manager
Senior Manager
avatar
Joined: 31 Aug 2009
Posts: 422
Location: Sydney, Australia
Followers: 6

Kudos [?]: 116 [0], given: 20

Re: Permutation / combinations [#permalink] New post 25 Sep 2009, 06:11
benjiboo wrote:
There are five flavors of icecream: banana, chocolate, lemon, strawberry and vanilla. You can have three scoops. How many variations will there be?






Why is the answer 35 (7!/3!x4!) and not 5^3 written like (5*5*5)=125?

Thank you


The reason you can't use 5x5x5 is that you will have duplicates. For example:
Banana Choc Lemon is essentially the same as Lemon, Choc, Banana and also Choc, Lemon, Banana.
So you do not duplicate it's easier to use the 7C3 formula which gives 35 (7!/3!x4!)
5 KUDOS received
Intern
Intern
User avatar
Joined: 27 Aug 2009
Posts: 46
Schools: London Business School
Followers: 4

Kudos [?]: 44 [5] , given: 1

Re: Permutation / combinations [#permalink] New post 25 Sep 2009, 08:58
5
This post received
KUDOS
benjiboo wrote:
There are five flavors of icecream: banana, chocolate, lemon, strawberry and vanilla. You can have three scoops. How many variations will there be?

Why is the answer 35 (7!/3!x4!) and not 5^3 written like (5*5*5)=125?
Thank you


Question 1
There are five flavors of icecream: banana, chocolate, lemon, strawberry and vanilla. You can have three scoops. How many variations will there be? (flavors cannot be repeated)
Answer
5C3 = 5!/(3! x 2!) = 10

Question 2
There are five flavors of icecream: banana, chocolate, lemon, strawberry and vanilla. You can have three scoops. How many variations will there be? (flavors can be repeated)
Answer
5 x 5 x 5 = 125

Question 3
There are five flavors of icecream: banana, chocolate, lemon, strawberry and vanilla. You can have three scoops. How many variations will there be? (flavors can be repeated but order doesn't matter)
Answer
(5+3-1)! / [3! x (5-1)!] = 35

From GMAT point of view, you need to know only first and second questions.

I am sure, 3rd question is not from any reputed GMAT related material.

There are many things, Permutation with repetition, Permutation without repetition, Combination with repetition, Combination without repetition. GMAT doesn't ask all the things. This will become very very complicated.

Still if u want to do research on question number 3, you can do that (but not for your GMAT exam). This question is about "Combination without repetition". So, here we can do repetitions. But point to be noted is that it is a combination problem. So, order doesn't matter.
Normally, when we take 5^3, order matters. So, BBL and BLB are different possibilities. But in 3rd question, BBL & BLB are same only (because order doesn't matter). This way, we need to proceed.
_________________

:good Salaries are low in recession. So, working for kudos now. :good

Senior Manager
Senior Manager
avatar
Joined: 31 Aug 2009
Posts: 422
Location: Sydney, Australia
Followers: 6

Kudos [?]: 116 [0], given: 20

Re: Permutation / combinations [#permalink] New post 25 Sep 2009, 14:35
Oops typo in the above. I believe its 5C3 as well. (5!/3!2!) not sure where I got 7 from :roll:
But I think TraderAK is right.
Intern
Intern
avatar
Joined: 24 Sep 2009
Posts: 23
Followers: 4

Kudos [?]: 69 [0], given: 2

Re: Permutation / combinations [#permalink] New post 25 Sep 2009, 14:44
yangsta8 wrote:
Oops typo in the above. I believe its 5C3 as well. (5!/3!2!) not sure where I got 7 from :roll:
But I think TraderAK is right.


the 7 was right. the 5 is wrong. There are 35 combination.
Intern
Intern
User avatar
Joined: 27 Aug 2009
Posts: 46
Schools: London Business School
Followers: 4

Kudos [?]: 44 [0], given: 1

Re: Permutation / combinations [#permalink] New post 25 Sep 2009, 21:34
benjiboo wrote:
yangsta8 wrote:
Oops typo in the above. I believe its 5C3 as well. (5!/3!2!) not sure where I got 7 from :roll:
But I think TraderAK is right.


the 7 was right. the 5 is wrong. There are 35 combination.


7C3 is not the solution.

Its just by chance that 7C3 is 35, which is matching with the answer 35 (answer to 3rd question).
_________________

:good Salaries are low in recession. So, working for kudos now. :good

Intern
Intern
avatar
Joined: 24 Sep 2009
Posts: 23
Followers: 4

Kudos [?]: 69 [0], given: 2

Re: Permutation / combinations [#permalink] New post 26 Sep 2009, 00:04
Here is from the original text:

Explanation to the problem:

Combination with repetition:

(n+r-1)! / r!(n-1)!

where n is the number of things to choose from, and you choose r of them
(Repetition allowed, order doesn't matter)

(5+3-1)! / 3!(5-1)! =

7! / 3! x 4! =

5040 / 6 x 24 =

35

-----
:shock: :( :cry: :oops:
Senior Manager
Senior Manager
avatar
Joined: 31 Aug 2009
Posts: 422
Location: Sydney, Australia
Followers: 6

Kudos [?]: 116 [0], given: 20

Re: Permutation / combinations [#permalink] New post 26 Sep 2009, 00:12
Hi Benjiboo where is this question from if you don't mind me asking?

I've never come across the formula:
(n+r-1)! / r!(n-1)!
Although that is probably due to my lack of knowledge.

The only two formulas I've come across in OG and Kaplan so far are the two standard formulas of
k!/n!(k-n)! and k!
Intern
Intern
avatar
Joined: 11 Aug 2009
Posts: 3
Followers: 0

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

Re: Permutation / combinations [#permalink] New post 29 Sep 2009, 02:26
TraderAK wrote:
benjiboo wrote:
There are five flavors of icecream: banana, chocolate, lemon, strawberry and vanilla. You can have three scoops. How many variations will there be?

Why is the answer 35 (7!/3!x4!) and not 5^3 written like (5*5*5)=125?
Thank you


Question 1
There are five flavors of icecream: banana, chocolate, lemon, strawberry and vanilla. You can have three scoops. How many variations will there be? (flavors cannot be repeated)
Answer
5C3 = 5!/(3! x 2!) = 10

Question 2
There are five flavors of icecream: banana, chocolate, lemon, strawberry and vanilla. You can have three scoops. How many variations will there be? (flavors can be repeated)
Answer
5 x 5 x 5 = 125

Question 3
There are five flavors of icecream: banana, chocolate, lemon, strawberry and vanilla. You can have three scoops. How many variations will there be? (flavors can be repeated but order doesn't matter)
Answer
(5+3-1)! / [3! x (5-1)!] = 35

From GMAT point of view, you need to know only first and second questions.

I am sure, 3rd question is not from any reputed GMAT related material.

There are many things, Permutation with repetition, Permutation without repetition, Combination with repetition, Combination without repetition. GMAT doesn't ask all the things. This will become very very complicated.

Still if u want to do research on question number 3, you can do that (but not for your GMAT exam). This question is about "Combination without repetition". So, here we can do repetitions. But point to be noted is that it is a combination problem. So, order doesn't matter.
Normally, when we take 5^3, order matters. So, BBL and BLB are different possibilities. But in 3rd question, BBL & BLB are same only (because order doesn't matter). This way, we need to proceed.


Agree with the great explanation given.
_________________

:m16 :teleport :plasma :m16 :teleport :plasma :m16 :teleport :plasma :m16 :teleport

Manager
Manager
avatar
Joined: 14 Dec 2008
Posts: 171
Followers: 1

Kudos [?]: 14 [0], given: 39

Re: Permutation / combinations [#permalink] New post 29 Sep 2009, 02:41
what is the solution to the original problem?.. :-)
1 KUDOS received
Intern
Intern
User avatar
Joined: 27 Aug 2009
Posts: 46
Schools: London Business School
Followers: 4

Kudos [?]: 44 [1] , given: 1

Re: Permutation / combinations [#permalink] New post 29 Sep 2009, 19:00
1
This post received
KUDOS
manojgmat wrote:
what is the solution to the original problem?.. :-)


In GMAT, if this question comes and its not clarified whether the flavors can be repeated or not, then u should assume that flavors can be repeated.
Answer will be 5*5*5 = 125

However, if there are 5 colored balls and we need to choose 3, and nothing is mentioned whether repetition is allowed or not. In that case, u should assume that balls are unique and each colored ball can not be repeated.
Answer will be 5C3 = 10


I think its clear what is the difference between these two examples. So, original question's answer is 125
_________________

:good Salaries are low in recession. So, working for kudos now. :good

Intern
Intern
avatar
Joined: 07 Oct 2009
Posts: 19
Followers: 0

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

Re: Permutation / combinations [#permalink] New post 15 Oct 2009, 02:51
The question can be solved with the use of the false coins method.

Now u have three scoops to choose and 5 diff flavours from which to choose from

So u need to put three good coins represented by "O" and 4 false coins represented by "X"

so now we have to arrange these three good coins and 4 false coins

This can be done in 7C3 ways

Now how will this solve the problem

Consider a combination

OOXXOXX

Any "O" left of the first X is the number of scoops of the first flavour = 2 scoops of flavour 1
Any "O" left of second X and right of first X is number of scoops of second flavour = 0 scoops of flavour 2
Similarly any "O" left of third and right of second X is number of scoops of third flavour = 1 scoops of flavour 3
Similarly any "O" left of Fourth and right of third X is number of scoops of fourth flavour = 0 scoops of flavour 4
Now finally any "O" right of fourth X is number of scoops of flavour 5 = 0 scoops of flavour 5 in this case


Similarly we can arrange as
XOXOXOX
Flavour 1 = 0
Flavour 2 = 1
Flavour 3 = 1
Flavour 4 = 1
Flavour 5 = 0

I hope this helps....


Similarly if there were 4 scoops to choose and 6 flavours the answer would be 9C4 as there would be 5 false coins ("X") and 4 good coins ("O") which we have to arrange.
CEO
CEO
User avatar
Joined: 09 Sep 2013
Posts: 2864
Followers: 207

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

Premium Member
Re: Permutation / combinations [#permalink] New post 15 Nov 2013, 05:04
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: Permutation / combinations   [#permalink] 15 Nov 2013, 05:04
    Similar topics Author Replies Last post
Similar
Topics:
1 Experts publish their posts in the topic In the standard formulation of a flavored drink the ratio by tejhpamarthi 5 15 Nov 2010, 06:01
1 For the best extraction of the flavor of saffron threads, it PTK 7 10 Sep 2010, 12:03
1 Experts publish their posts in the topic Albert sells chocolate ice-cream for $0.15 per cup and sondenso 3 23 May 2008, 01:51
PS: ice-cream sign sgoll 7 13 Feb 2007, 07:41
PS - Icecream Priti 7 15 Aug 2005, 07:17
Display posts from previous: Sort by

There are five flavors of icecream: banana, chocolate, lemon

  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®.