GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 12 Jul 2020, 22:25

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 ways can 6 different letters be posted in 3 letterboxes su

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

Hide Tags

Find Similar Topics 
GMAT Club Legend
GMAT Club Legend
User avatar
V
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 4350
Location: India
GMAT: QUANT EXPERT
Schools: IIM (A)
GMAT 1: 750 Q51 V41
WE: Education (Education)
Reviews Badge
In how many ways can 6 different letters be posted in 3 letterboxes su  [#permalink]

Show Tags

New post 04 Jun 2020, 22:26
1
8
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

52% (02:16) correct 48% (02:06) wrong based on 25 sessions

HideShow timer Statistics

In how many ways can 6 different letters be posted in 3 letterboxes such that each box receives atleast 1 letter?

(A) 120
(B) 180
(C) 360
(D) 540
(E) 720


_________________
Prepare with PERFECTION to claim Q≥50 and V≥40 !!!
GMATinsight .............(Bhoopendra Singh and Dr.Sushma Jha)
e-mail: info@GMATinsight.com l Call : +91-9999687183 / 9891333772
One-on-One Skype classes l Classroom Coaching l On-demand Quant course l Admissions Consulting

Most affordable l Comprehensive l 2000+ Qn ALL with Video explanations l LINK: Courses and Pricing
Click for FREE Demo on VERBAL & QUANT
Our SUCCESS STORIES: From 620 to 760 l Q-42 to Q-49 in 40 days l 590 to 710 + Wharton l
FREE GMAT Resource: 22 FREE (FULL LENGTH) GMAT CATs LINKS l NEW OG QUANT 50 Qn+VIDEO Sol.
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 18 Aug 2017
Posts: 6442
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
In how many ways can 6 different letters be posted in 3 letterboxes su  [#permalink]

Show Tags

New post 05 Jun 2020, 12:10
2
Total possible arrangement to arrange 6 letters in 3 letter boxes such that each box has 1 letter
4,1,1 ; 3,2,1 ; 2,2,2
Ways to arrange
4,1,1= 6!/4!*1*1*2! = 15
3,2,1= 6!/3!*2! = 60
2,2,2= 6!/2!*2!*2!*3!= 15
Total 15+15+60;90
And letter boxes can be arranged in 3! Ways so 90*3!= 540
Option D

GMATinsight
sir please provide solution considering
(total cases- unwanted cases)
I tried solving making unwanted cases but not getting answer..
6,0,0
5,1,0
3,3,0
4,2,0



GMATinsight wrote:
In how many ways can 6 different letters be posted in 3 letterboxes such that each box receives atleast 1 letter?

(A) 120
(B) 180
(C) 360
(D) 540
(E) 720



Posted from my mobile device
Senior Manager
Senior Manager
avatar
S
Joined: 18 Dec 2017
Posts: 300
Re: In how many ways can 6 different letters be posted in 3 letterboxes su  [#permalink]

Show Tags

New post 05 Jun 2020, 18:34
1
First solution
4,1,1
Can be taken in 3 ways
Now letters can be chosen in
6C4×2C1×1C1= 15×2×1=30
Total number of ways =30×3=90
Second solution
1,2,3
Can be taken in 6 ways
Now letters can be chosen in
6C1×5C2×3C3= 6×10×1= 60
Total number of ways =6×60=360
Third solution
2,2,2
Can be taken in 1 way
Now letters can be chosen in
6C2×4C2×2C2= 15×6×1 =90
Total number of ways =90×1 =90
Total of all possible solutions=
90+360+90=540
Option D is the answer

Posted from my mobile device
GMAT Club Legend
GMAT Club Legend
User avatar
V
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 4350
Location: India
GMAT: QUANT EXPERT
Schools: IIM (A)
GMAT 1: 750 Q51 V41
WE: Education (Education)
Reviews Badge
In how many ways can 6 different letters be posted in 3 letterboxes su  [#permalink]

Show Tags

New post 05 Jun 2020, 21:47
1
1
GMATinsight wrote:
In how many ways can 6 different letters be posted in 3 letterboxes such that each box receives atleast 1 letter?

(A) 120
(B) 180
(C) 360
(D) 540
(E) 720



Method-1:



Distribution of letters can happen in three ways (4-1-1) (2-2-2) and (3-2-1) ways

Case 1: 3-2-1 = 6C3*3C2*3! = 360

Case 2: 2-2-2 = 6C2*4C2 = 15*6 = 90

Case 3: 4-1-1 = 6C4*3! = 90

Total Ways = 360+90+90 = 540

Answer: Option D


Method-2:


Archit3110

Favourable Cases = Total cases - Unwanted cases

Total ways of distribution of 6 letters = 3*3*3*3*3*3 = 729

Unwanted cases = Atleast one box gets zero letter = 3C1*(2^6-1) = 3*63 = 189
3C1 = Ways to select the box that gets zero letter
2^6 = Total ways of distributing 6 letters into remaining 2 boxes with each letter having 2 choices Letter box 1 or box 2
-1 = Removing a case in which only one box receives all letters (counted twice due to 3C1)

i.e. Favourable cases = 729 - 189 = 540

Answer: Option D


Method-3:



6,0,0 = 3 ways
5,1,0 = 3C2*6C5*2! = 36 ways
3,3,0 = 3C2*6C3 = 60 ways
4,2,0 = 3C2*6C4*2! = 90 ways

So unfavorable cases = 3+36+60+90 = 189
Total ways of distribution of 6 letters = 3*3*3*3*3*3 = 729
i.e. Favourable cases = 729 - 189 = 540

Answer: Option D

_________________
Prepare with PERFECTION to claim Q≥50 and V≥40 !!!
GMATinsight .............(Bhoopendra Singh and Dr.Sushma Jha)
e-mail: info@GMATinsight.com l Call : +91-9999687183 / 9891333772
One-on-One Skype classes l Classroom Coaching l On-demand Quant course l Admissions Consulting

Most affordable l Comprehensive l 2000+ Qn ALL with Video explanations l LINK: Courses and Pricing
Click for FREE Demo on VERBAL & QUANT
Our SUCCESS STORIES: From 620 to 760 l Q-42 to Q-49 in 40 days l 590 to 710 + Wharton l
FREE GMAT Resource: 22 FREE (FULL LENGTH) GMAT CATs LINKS l NEW OG QUANT 50 Qn+VIDEO Sol.
Stern School Moderator
User avatar
S
Joined: 26 May 2020
Posts: 273
Concentration: General Management, Technology
Schools: NYU Stern, LBS
WE: Analyst (Computer Software)
CAT Tests
Re: In how many ways can 6 different letters be posted in 3 letterboxes su  [#permalink]

Show Tags

New post 05 Jun 2020, 22:20
GMATinsight wrote:
GMATinsight wrote:
In how many ways can 6 different letters be posted in 3 letterboxes such that each box receives atleast 1 letter?

(A) 120
(B) 180
(C) 360
(D) 540
(E) 720



Method-1:



Distribution of letters can happen in three ways (4-1-1) (2-2-2) and (3-2-1) ways

Case 1: 3-2-1 = 6C3*3C2*3! = 360

Case 2: 2-2-2 = 6C2*4C2 = 15*6 = 90

Case 3: 4-1-1 = 6C4*3! = 90

Total Ways = 360+90+90 = 540

Answer: Option D


Method-2:


Archit3110

Favourable Cases = Total cases - Unwanted cases

Total ways of distribution of 6 letters = 3*3*3*3*3*3 = 729

Unwanted cases = Atleast one box gets zero letter = 3C1*(2^6-1) = 3*63 = 189
3C1 = Ways to select the box that gets zero letter
2^6 = Total ways of distributing 6 letters into remaining 2 boxes with each letter having 2 choices Letter box 1 or box 2
-1 = Removing a case in which only one box receives all letters (counted twice due to 3C1)

i.e. Favourable cases = 729 - 189 = 540

Answer: Option D


Method-3:



6,0,0 = 3 ways
5,1,0 = 3C2*6C5*2! = 36 ways
3,3,0 = 3C2*6C3 = 60 ways
4,2,0 = 3C2*6C4*2! = 90 ways

So unfavorable cases = 3+36+60+90 = 189
Total ways of distribution of 6 letters = 3*3*3*3*3*3 = 729
i.e. Favourable cases = 729 - 189 = 540

Answer: Option D


Can we not use partition concept of combination in this case ..
_________________
Thank you.
Regards,
Ashish A Das.

The more realistic you are during your practice, the more confident you will be during the CAT.
GMAT Club Legend
GMAT Club Legend
User avatar
V
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 4350
Location: India
GMAT: QUANT EXPERT
Schools: IIM (A)
GMAT 1: 750 Q51 V41
WE: Education (Education)
Reviews Badge
Re: In how many ways can 6 different letters be posted in 3 letterboxes su  [#permalink]

Show Tags

New post 05 Jun 2020, 22:57
1
DasAshishAshutosh

Partition rule for the similar objects to be arranged.

this question specifically mentions that 6 letters are different so NO, we can not use partition method here. :)

Hope it help! :)

DasAshishAshutosh wrote:
GMATinsight wrote:
GMATinsight wrote:
In how many ways can 6 different letters be posted in 3 letterboxes such that each box receives atleast 1 letter?

(A) 120
(B) 180
(C) 360
(D) 540
(E) 720



Method-1:



Distribution of letters can happen in three ways (4-1-1) (2-2-2) and (3-2-1) ways

Case 1: 3-2-1 = 6C3*3C2*3! = 360

Case 2: 2-2-2 = 6C2*4C2 = 15*6 = 90

Case 3: 4-1-1 = 6C4*3! = 90

Total Ways = 360+90+90 = 540

Answer: Option D


Method-2:


Archit3110

Favourable Cases = Total cases - Unwanted cases

Total ways of distribution of 6 letters = 3*3*3*3*3*3 = 729

Unwanted cases = Atleast one box gets zero letter = 3C1*(2^6-1) = 3*63 = 189
3C1 = Ways to select the box that gets zero letter
2^6 = Total ways of distributing 6 letters into remaining 2 boxes with each letter having 2 choices Letter box 1 or box 2
-1 = Removing a case in which only one box receives all letters (counted twice due to 3C1)

i.e. Favourable cases = 729 - 189 = 540

Answer: Option D


Method-3:



6,0,0 = 3 ways
5,1,0 = 3C2*6C5*2! = 36 ways
3,3,0 = 3C2*6C3 = 60 ways
4,2,0 = 3C2*6C4*2! = 90 ways

So unfavorable cases = 3+36+60+90 = 189
Total ways of distribution of 6 letters = 3*3*3*3*3*3 = 729
i.e. Favourable cases = 729 - 189 = 540

Answer: Option D


Can we not use partition concept of combination in this case ..


Posted from my mobile device
_________________
Prepare with PERFECTION to claim Q≥50 and V≥40 !!!
GMATinsight .............(Bhoopendra Singh and Dr.Sushma Jha)
e-mail: info@GMATinsight.com l Call : +91-9999687183 / 9891333772
One-on-One Skype classes l Classroom Coaching l On-demand Quant course l Admissions Consulting

Most affordable l Comprehensive l 2000+ Qn ALL with Video explanations l LINK: Courses and Pricing
Click for FREE Demo on VERBAL & QUANT
Our SUCCESS STORIES: From 620 to 760 l Q-42 to Q-49 in 40 days l 590 to 710 + Wharton l
FREE GMAT Resource: 22 FREE (FULL LENGTH) GMAT CATs LINKS l NEW OG QUANT 50 Qn+VIDEO Sol.
Stern School Moderator
User avatar
S
Joined: 26 May 2020
Posts: 273
Concentration: General Management, Technology
Schools: NYU Stern, LBS
WE: Analyst (Computer Software)
CAT Tests
Re: In how many ways can 6 different letters be posted in 3 letterboxes su  [#permalink]

Show Tags

New post 05 Jun 2020, 23:34
GMATinsight wrote:
DasAshishAshutosh

Partition rule for the similar objects to be arranged.

this question specifically mentions that 6 letters are different so NO, we can not use partition method here. :)

Hope it help! :)

Yes . Thanks GMATinsight
_________________
Thank you.
Regards,
Ashish A Das.

The more realistic you are during your practice, the more confident you will be during the CAT.
GMAT Club Bot
Re: In how many ways can 6 different letters be posted in 3 letterboxes su   [#permalink] 05 Jun 2020, 23:34

In how many ways can 6 different letters be posted in 3 letterboxes su

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





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