GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 21 Mar 2019, 11:11

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.

Close

Request Expert Reply

Confirm Cancel

In how many different ways can 3 identical green shirts and

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
Senior Manager
Senior Manager
avatar
Status: Do and Die!!
Joined: 15 Sep 2010
Posts: 260
In how many different ways can 3 identical green shirts and  [#permalink]

Show Tags

New post Updated on: 24 Feb 2012, 22:58
3
12
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

66% (01:16) correct 34% (01:36) wrong based on 288 sessions

HideShow timer Statistics

In how many different ways can 3 identical green shirts and 3 identical red shirts be distributed among 6 children such that each child receives a shirt?

A. 20
B. 40
C. 216
D. 720
E. 729

_________________

I'm the Dumbest of All !!


Originally posted by shrive555 on 25 Nov 2010, 18:54.
Last edited by Bunuel on 24 Feb 2012, 22:58, edited 1 time in total.
Edited the question
Director
Director
User avatar
Joined: 03 Sep 2006
Posts: 777
GMAT ToolKit User
Re: Combination  [#permalink]

Show Tags

New post 25 Nov 2010, 19:51
2
2
GGG RRR

Therefore total number of ways is

6! but there are two groups of 3 identical things.

Therefore total number of "different" ways is

6!/ (3!) (3!) = 20
Intern
Intern
avatar
Joined: 21 Jun 2010
Posts: 4
Re: Combination  [#permalink]

Show Tags

New post 25 Nov 2010, 20:01
No of ways 6 shirts can be distributed among 6 people 6!
Since 3 red are identical and 3 green are identical = (6!)/3!*3!=20
Veritas Prep GMAT Instructor
User avatar
D
Joined: 16 Oct 2010
Posts: 8998
Location: Pune, India
Re: Combination  [#permalink]

Show Tags

New post 25 Nov 2010, 21:43
2
shrive555 wrote:
In how many different ways can 3 identical green shirts and 3 identical red shirts be distributed among 6 children such that each child receives a shirt?

20
40
216
720
729


Or out of 6 children, choose 3 in 6C3 ways = 20 ways.

Note: When you choose 3 children say, A, B and C are give them a red shirt, D, E and F get a green shirt. When you choose D, E and F and give them a red shirt, A, B and C automatically get the green shirts. So you do not need to multiply by 2! above.
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

Intern
Intern
avatar
Joined: 24 Feb 2012
Posts: 31
Re: Combination  [#permalink]

Show Tags

New post 24 Feb 2012, 17:19
Approach 1:
1st Child: 6 has options
2nd Child: 5 has options…
Therefore, for all kids: 6 x 5 x 4 x 3 x 2 = 720 arrangements.

Since the reds are identical, we divide by 3!; Since the greens are identical, we divide by another 3!

So: in all, 720/[ 3! X 3! ] = 20 ways.

Approach 2 / MGMAT technique:
This is like anagramming RRRGGG. No of arrangements = 6! / 3! x 3! ways ==> 20.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 53771
Re: In how many different ways can 3 identical green shirts and  [#permalink]

Show Tags

New post 24 Feb 2012, 22:59
3
1
shrive555 wrote:
In how many different ways can 3 identical green shirts and 3 identical red shirts be distributed among 6 children such that each child receives a shirt?

A. 20
B. 40
C. 216
D. 720
E. 729


1-2-3-4-5-6 (children)
B-B-B-G-G-G (shirts)
G-B-B-G-G-B
G-G-B-G-B-B
....

So, basically # of assignments of 6 shirts to 6 children (such that each child receives a shirt) equals to # of permutations of 6 letters BBBGGG, which is \(\frac{6!}{3!3!}=20\) (we divide by 3!*3!, since there are 3 identical B's and 3 identical G's).

Answer: A.

Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Director
Director
User avatar
G
Joined: 23 Jan 2013
Posts: 551
Schools: Cambridge'16
In how many different ways can 3 identical green shirts and  [#permalink]

Show Tags

New post 30 Mar 2015, 01:18
What if we distribute 6 shirts among 4 children?

R-R-R-G-G-G (shirts)
1-2-3-4 (children)

RRRG
RRGG
RGGG
GGGR
GGRR
GRRR
RGRG
GRGR
RGGR
GRRG

Looks like 10

algebraically 6*5*4*3/3! *3!=10

Is that right?
Veritas Prep GMAT Instructor
User avatar
D
Joined: 16 Oct 2010
Posts: 8998
Location: Pune, India
Re: In how many different ways can 3 identical green shirts and  [#permalink]

Show Tags

New post 30 Mar 2015, 01:55
Temurkhon wrote:
What if we distribute 6 shirts among 4 children?

R-R-R-G-G-G (shirts)
1-2-3-4 (children)

RRRG
RRGG
RGGG
GGGR
GGRR
GRRR
RGRG
GRGR
RGGR
GRRG

Looks like 10

algebraically 6*5*4*3/3! *3!=10

Is that right?


You mean each child gets exactly one shirt?

You have missed 4 cases: GRGG, GGRG, RGRR, RRGR

There will be total 14 cases.
Say, had there been 4 of each type of shirt, each child could have got a shirt in two ways: Red or Green. This would give us 2*2*2*2 = 16 ways.
But "All 4 children get Red" and "All 4 children get Green" are two cases which are not possible. So total cases are 16 - 2 = 14
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

Director
Director
User avatar
G
Joined: 23 Jan 2013
Posts: 551
Schools: Cambridge'16
Re: In how many different ways can 3 identical green shirts and  [#permalink]

Show Tags

New post 30 Mar 2015, 02:07
Karishma,

thanks for immediate response. I'm confined by one concept
Director
Director
User avatar
G
Joined: 23 Jan 2013
Posts: 551
Schools: Cambridge'16
In how many different ways can 3 identical green shirts and  [#permalink]

Show Tags

New post 30 Mar 2015, 03:36
What about 6 shirts and 5 children?

My view is that we have two options to be distributed:

3 Red shirts and 2 Green shirts

OR

2 Red shirts and 3 Green shirts

5!/3!*2!=10*2=20

What do you think, Karishma. I'm sorry to be annoying
CEO
CEO
User avatar
V
Joined: 12 Sep 2015
Posts: 3515
Location: Canada
Re: In how many different ways can 3 identical green shirts and  [#permalink]

Show Tags

New post 29 Aug 2016, 14:14
3
Top Contributor
1
shrive555 wrote:
In how many different ways can 3 identical green shirts and 3 identical red shirts be distributed among 6 children such that each child receives a shirt?

A. 20
B. 40
C. 216
D. 720
E. 729

We can take this question and ask an easier question: In how many ways can we choose 3 of the 6 children to receive a green shirt?

Notice that, once we have given a green shirt to each of those 3 chosen children, the REMAINING 3 children must get red shirts. In other words, once we have given green shirts to 3 children, the children who get red shirts is locked.

So, in how many ways can we select 3 of the 6 children to receive a green shirt?
Since the order of the selected children does not matter, this is a combination question.
We can choose 3 children from 6 children in 6C3 ways (= 20 ways)

Answer:

RELATED VIDEOS



_________________

Test confidently with gmatprepnow.com
Image

Manager
Manager
User avatar
B
Joined: 30 Oct 2012
Posts: 62
Location: India
WE: Marketing (Manufacturing)
Premium Member
Re: In how many different ways can 3 identical green shirts and  [#permalink]

Show Tags

New post 29 Aug 2016, 19:15
shrive555 wrote:
In how many different ways can 3 identical green shirts and 3 identical red shirts be distributed among 6 children such that each child receives a shirt?

A. 20
B. 40
C. 216
D. 720
E. 729


6! / 3!x3! = 120/6= 20 ways
_________________

i am the master of my fate, I am the captain of my soul

Current Student
User avatar
B
Status: DONE!
Joined: 05 Sep 2016
Posts: 372
Re: In how many different ways can 3 identical green shirts and  [#permalink]

Show Tags

New post 17 Nov 2016, 19:39
6!/3!3! = 20 --> Combination that takes into account two items (in this case, shirts), that are identical.

A.
Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 5381
Location: United States (CA)
Re: In how many different ways can 3 identical green shirts and  [#permalink]

Show Tags

New post 29 Nov 2016, 16:28
shrive555 wrote:
In how many different ways can 3 identical green shirts and 3 identical red shirts be distributed among 6 children such that each child receives a shirt?

A. 20
B. 40
C. 216
D. 720
E. 729


If we let G denote a green shirt and R denote a red shirt, the problem becomes how to arrange 3 Gs and 3 Rs in the string of GGGRRR. The answer can be found using the concept of permutations with repetition of indistinguishable objects, using the following formula:

Image

In this formula, N represents the total number of objects to be arranged. Each ri (i = 1, 2, 3, …, n) represents the frequency of each of the i indistinguishable objects.

The frequency simply means the number of times that the indistinguishable item occurs in the set. Note that there are 3 green shirts that are identical (indistinguishable), and there are 3 red shirts that are identical (indistinguishable).

Therefore, the number of ways we can arrange 3 Gs and 3 Rs in the string of GGGRRR is:

6!/(3! × 3!) = 720/(6 × 6) = 720/36 = 20

Answer: A
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13768
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: In how many different ways can 3 identical green shirts and  [#permalink]

Show Tags

New post 13 Feb 2018, 22:58
Hi All,

If we had 6 different shirts, then there would be 6! = 720 options. However, since there are 3 IDENTICAL red shirts and 3 IDENTICAL green shirts, we have to do some extra work on our calculations.

If we call 3 of the children A, B and C and each of them gets an identical red shirt, then there are technically 6 different ways for those 3 shirts to be given to those 3 children. Since the shirts are identical though, we are NOT supposed to count this as 6 different options....it should only be counted as 1 option.

Thus, we would have to divide 720 by 6....

We would have to do the same thing with the identical green shirts, which means we'd have to divide by 6 AGAIN.

720/6 = 120
120/6 = 20

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 10166
Premium Member
Re: In how many different ways can 3 identical green shirts and  [#permalink]

Show Tags

New post 10 Mar 2019, 05:38
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

GMAT Club Bot
Re: In how many different ways can 3 identical green shirts and   [#permalink] 10 Mar 2019, 05:38
Display posts from previous: Sort by

In how many different ways can 3 identical green shirts and

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

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

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.