Last visit was: 15 Jul 2025, 16:12 It is currently 15 Jul 2025, 16:12
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
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 15 Jul 2025
Posts: 102,582
Own Kudos:
Given Kudos: 98,190
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,582
Kudos: 741,696
 [22]
4
Kudos
Add Kudos
18
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
Gnpth
Joined: 29 Aug 2012
Last visit: 03 Mar 2023
Posts: 1,049
Own Kudos:
6,616
 [7]
Given Kudos: 330
Status:Chasing my MBB Dream!
Location: United States (DC)
WE:General Management (Aerospace and Defense)
Products:
Posts: 1,049
Kudos: 6,616
 [7]
3
Kudos
Add Kudos
4
Bookmarks
Bookmark this Post
General Discussion
User avatar
shelrod007
Joined: 23 Jan 2013
Last visit: 16 Sep 2016
Posts: 99
Own Kudos:
Given Kudos: 41
Concentration: Technology, Other
Schools: Berkeley Haas
GMAT Date: 01-14-2015
WE:Information Technology (Computer Software)
Schools: Berkeley Haas
Posts: 99
Kudos: 185
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 14 Jul 2025
Posts: 11,294
Own Kudos:
Given Kudos: 333
Status:Math and DI Expert
Products:
Expert
Expert reply
Posts: 11,294
Kudos: 41,763
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
A retail company needs to set up five additional distribution centers that can be located in three cities on the east coast (Boston, New York, and Washington, D.C.), one city in the Midwest (Chicago), and three cities on the west coast (Seattle, San Francisco, and Los Angeles). If the company must add two distribution centers on each coast and one in the Midwest, and only one center can be added in each city, in how many ways can the management allocate the distribution centers?

A. 3
B. 9
C. 18
D. 20
E. 36

Kudos for a correct solution.
in west coast 2out of 3
in east coast 2out of 3
and mid west 1 of 1..
total ways 3c2*3c2*1c1=9.. ans B
avatar
Wonder1
Joined: 27 Apr 2015
Last visit: 14 Dec 2019
Posts: 13
Own Kudos:
Given Kudos: 114
Location: India
Concentration: Technology, Marketing
Schools: ISB '18 (A)
GMAT 1: 740 Q50 V39
GPA: 3.2
Schools: ISB '18 (A)
GMAT 1: 740 Q50 V39
Posts: 13
Kudos: 1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Cant we have 3 on east coast and only one on the west.



chetan2u
Bunuel
A retail company needs to set up five additional distribution centers that can be located in three cities on the east coast (Boston, New York, and Washington, D.C.), one city in the Midwest (Chicago), and three cities on the west coast (Seattle, San Francisco, and Los Angeles). If the company must add two distribution centers on each coast and one in the Midwest, and only one center can be added in each city, in how many ways can the management allocate the distribution centers?

A. 3
B. 9
C. 18
D. 20
E. 36

Kudos for a correct solution.
in west coast 2out of 3
in east coast 2out of 3
and mid west 1 of 1..
total ways 3c2*3c2*1c1=9.. ans B
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 14 Jul 2025
Posts: 11,294
Own Kudos:
41,763
 [1]
Given Kudos: 333
Status:Math and DI Expert
Products:
Expert
Expert reply
Posts: 11,294
Kudos: 41,763
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
shravanthim
Cant we have 3 on east coast and only one on the west.



chetan2u
Bunuel
A retail company needs to set up five additional distribution centers that can be located in three cities on the east coast (Boston, New York, and Washington, D.C.), one city in the Midwest (Chicago), and three cities on the west coast (Seattle, San Francisco, and Los Angeles). If the company must add two distribution centers on each coast and one in the Midwest, and only one center can be added in each city, in how many ways can the management allocate the distribution centers?

A. 3
B. 9
C. 18
D. 20
E. 36

Kudos for a correct solution.
in west coast 2out of 3
in east coast 2out of 3
and mid west 1 of 1..
total ways 3c2*3c2*1c1=9.. ans B

Hi,
NO, we have to choose two in each coast since it is given the coast..
Quote:
If the company must add two distribution centers on each coast and one in the Midwest,
..

had the wordings been ..
If the company must add one distribution centers in the Midwest, and only one center can be added in each city, in how many ways can the management allocate the distribution centers?
in that case the WAY mentioned by you will also come into play..


Hope it helped
User avatar
Nevernevergiveup
User avatar
Retired Moderator
Joined: 18 Sep 2014
Last visit: 20 Aug 2023
Posts: 1,009
Own Kudos:
Given Kudos: 79
Location: India
Products:
Posts: 1,009
Kudos: 2,950
Kudos
Add Kudos
Bookmarks
Bookmark this Post
chetan2u
shravanthim
Cant we have 3 on east coast and only one on the west.
chetan2u
in west coast 2out of 3
in east coast 2out of 3
and mid west 1 of 1..
total ways 3c2*3c2*1c1=9.. ans B

Hi,
NO, we have to choose two in each coast since it is given the coast..
Quote:
If the company must add two distribution centers on each coast and one in the Midwest,
..

had the wordings been ..
If the company must add one distribution centers in the Midwest, and only one center can be added in each city, in how many ways can the management allocate the distribution centers?
in that case the WAY mentioned by you will also come into play..


Hope it helped

Hi chetan2u

can you elaborate? I have a similar doubt. We need to pick two centers in each coast as per the question.
I think as below
1st distribution center in east coast can have 3 choices
2nd distribution center in east coast can have 2 choices
Similar case with west coast.
Whats wrong with my thinking?
avatar
ASredhar
Joined: 19 Feb 2013
Last visit: 02 Feb 2017
Posts: 1
Own Kudos:
Given Kudos: 81
Location: India
GMAT 1: 610 Q43 V31
Products:
GMAT 1: 610 Q43 V31
Posts: 1
Kudos: 6
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I solved this question the same way:

East Coast : 3x2 (and) West Coast: 3x2 (and) Midwest 1 = 36

Please do point out the error in this logic.

Regards,
Arvind.
avatar
matsuda
Joined: 08 Mar 2016
Last visit: 23 Dec 2016
Posts: 11
Own Kudos:
11
 [1]
Given Kudos: 6
Posts: 11
Kudos: 11
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ASredhar
I solved this question the same way:

East Coast : 3x2 (and) West Coast: 3x2 (and) Midwest 1 = 36

Please do point out the error in this logic.

Regards,
Arvind.

This way you are considering that the order of the cities in each coast matters, when it actually doesn't.

It doesn't matter if your picks are:

NY Boston Chicago LA SF

or

Boston NY Chicago LA SF

The cities picked are still the same.
User avatar
daboo343
Joined: 09 Nov 2012
Last visit: 20 Nov 2022
Posts: 223
Own Kudos:
692
 [1]
Given Kudos: 162
Status:You have to have the darkness for the dawn to come
Daboo: Sonu
GMAT 1: 590 Q49 V20
GMAT 2: 730 Q50 V38
Products:
GMAT 2: 730 Q50 V38
Posts: 223
Kudos: 692
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
A retail company needs to set up five additional distribution centers that can be located in three cities on the east coast (Boston, New York, and Washington, D.C.), one city in the Midwest (Chicago), and three cities on the west coast (Seattle, San Francisco, and Los Angeles). If the company must add two distribution centers on each coast and one in the Midwest, and only one center can be added in each city, in how many ways can the management allocate the distribution centers?

A. 3
B. 9
C. 18
D. 20
E. 36

Kudos for a correct solution.

In east coast 3C2 ways..................1
In west coast 3C2 ways..................2
In midwest 1C1 ways ...................3
total= 1*2*3
=9
hence B
avatar
ehsan090
Joined: 08 Oct 2016
Last visit: 16 Feb 2018
Posts: 179
Own Kudos:
Given Kudos: 76
Location: United States
Concentration: General Management, Finance
GPA: 2.9
WE:Engineering (Telecommunications)
Posts: 179
Kudos: 44
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Answer is B.. Get is 1:24 should be less though
East coast*Mid coast*west coast
3c2*1c1*3c2
3*1*3
9
avatar
Shobhit7
Joined: 01 Feb 2017
Last visit: 29 Apr 2021
Posts: 241
Own Kudos:
Given Kudos: 148
Posts: 241
Kudos: 397
Kudos
Add Kudos
Bookmarks
Bookmark this Post
There are 5 Centres and 7 Cities ( EC:3, WC:3, MW:1).
Constraints: 2 Centres affixed to EC; 2 Centres affixed to WC ; 1 Centre affixed to MW.
Ways to Distribute Centres: MW- 1 ; EC: 3C2 ; WC: 3C2.
Hence, Total ways= MW x EC x WC = 1 × 3 × 3 = 9.
Correct Choice: B
User avatar
Nunuboy1994
Joined: 12 Nov 2016
Last visit: 24 Apr 2019
Posts: 559
Own Kudos:
Given Kudos: 167
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
Posts: 559
Kudos: 122
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
A retail company needs to set up five additional distribution centers that can be located in three cities on the east coast (Boston, New York, and Washington, D.C.), one city in the Midwest (Chicago), and three cities on the west coast (Seattle, San Francisco, and Los Angeles). If the company must add two distribution centers on each coast and one in the Midwest, and only one center can be added in each city, in how many ways can the management allocate the distribution centers?

A. 3
B. 9
C. 18
D. 20
E. 36

Kudos for a correct solution.

We don't necessarily need to factor in the midwest city since there is only one possibility for it; now, actually, the most logical way to think of the problem is that there are three cities that will have or rather choose 2 cities among the 4 cities remaining instead of thinking 4 cities choose 2 spots-

3c2 x 3c2 = 9
User avatar
chipsy
Joined: 05 Oct 2014
Last visit: 01 Sep 2021
Posts: 55
Own Kudos:
Given Kudos: 149
Concentration: Technology, Entrepreneurship
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The management allocate the distribution centers in : 3C2 * 1C1 * 3C2 = 9

the answer is option B.

Bunuel : please provide the OA after review.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 15 Jul 2025
Posts: 102,582
Own Kudos:
Given Kudos: 98,190
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,582
Kudos: 741,696
Kudos
Add Kudos
Bookmarks
Bookmark this Post
chipsy
The management allocate the distribution centers in : 3C2 * 1C1 * 3C2 = 9

the answer is option B.

Bunuel : please provide the OA after review.
________________
The OA is B.
User avatar
warriorguy
User avatar
Retired Moderator
Joined: 04 Aug 2016
Last visit: 08 Feb 2023
Posts: 379
Own Kudos:
Given Kudos: 144
Location: India
Concentration: Leadership, Strategy
GPA: 4
WE:Engineering (Telecommunications)
Posts: 379
Kudos: 351
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Nevernevergiveup

Hi chetan2u

can you elaborate? I have a similar doubt. We need to pick two centers in each coast as per the question.
I think as below
1st distribution center in east coast can have 3 choices
2nd distribution center in east coast can have 2 choices
Similar case with west coast.
Whats wrong with my thinking?

Hi Nevernevergiveup,

If i understood correctly, you would also need to divide by 2! in order to account for any false counts i.e. duplicates. So you would end with 3 such cases per coast.
User avatar
EMPOWERgmatRichC
User avatar
Major Poster
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,788
Own Kudos:
12,494
 [1]
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,788
Kudos: 12,494
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Hi ALL,

While this question IS wordy, it's really just a Combination Formula question (albeit with a lot of little pieces of information).

By reorganizing the information in the prompt, we are told the following:

1) There are 3 cities on the East Coast; we must put a distribution center in 2 of them.
2) There is 1 city in the Midwest; we must put a distribution center there.
3) There are 3 cities on the West Coast; we must put a distribution center in 2 of them.

Since the "order" of the distribution centers does NOT matter, we're dealing with a Combinatorics situation.

East Coast: 3c2 = 3!/[2!1!] = 3 ways to place the distribution centers
Midwest: 1c1 = 1 way to place the distribution center
West Coast: 3c2 = 3!/[2!1!] = 3 ways to place the distribution centers

We have to multiply these results to calculate the TOTAL possible combinations of distribution centers:

(3)(1)(3) = 9 different ways to place the distribution centers.

Final Answer:

GMAT assassins aren't born, they're made,
Rich
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,412
Own Kudos:
Posts: 37,412
Kudos: 1,013
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Moderators:
Math Expert
102582 posts
PS Forum Moderator
695 posts