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# A retail company needs to set up five additional distribution centers

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Math Expert
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A retail company needs to set up five additional distribution centers  [#permalink]

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20 Jan 2015, 05:38
3
11
00:00

Difficulty:

35% (medium)

Question Stats:

74% (01:50) correct 26% (02:20) wrong based on 268 sessions

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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.

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Re: A retail company needs to set up five additional distribution centers  [#permalink]

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20 Jan 2015, 22:03
2
Bunuel wrote:
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.

2 distributors in east coast and 2 in west coast. And 1 in Midwest.

So,

East Coast= 3C2: $$\frac{3!}{2!1!}$$= 3.

West Coast= 3C2: $$\frac{3!}{2!1!}$$= 3.

Midwest= 1C1= 1

So The total number of ways will be,

$$3*1*3= 9$$.

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Re: A retail company needs to set up five additional distribution centers  [#permalink]

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08 Feb 2015, 02:00
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 Combinations 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.
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Re: A retail company needs to set up five additional distribution centers  [#permalink]

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08 Feb 2015, 02:15
Bunuel wrote:
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
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Re: A retail company needs to set up five additional distribution centers  [#permalink]

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06 Apr 2016, 00:35
Cant we have 3 on east coast and only one on the west.

chetan2u wrote:
Bunuel wrote:
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
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Posts: 7036
Re: A retail company needs to set up five additional distribution centers  [#permalink]

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06 Apr 2016, 00:55
shravanthim wrote:
Cant we have 3 on east coast and only one on the west.

chetan2u wrote:
Bunuel wrote:
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,
..

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
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: A retail company needs to set up five additional distribution centers  [#permalink]

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12 Jul 2016, 04:03
chetan2u wrote:
shravanthim wrote:
Cant we have 3 on east coast and only one on the west.
chetan2u wrote:
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,
..

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?
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Re: A retail company needs to set up five additional distribution centers  [#permalink]

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14 Jul 2016, 03:48
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.
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Re: A retail company needs to set up five additional distribution centers  [#permalink]

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21 Jul 2016, 12:21
ASredhar wrote:
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.
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Re: A retail company needs to set up five additional distribution centers  [#permalink]

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02 Apr 2017, 09:58
1
Bunuel wrote:
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
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Re: A retail company needs to set up five additional distribution centers  [#permalink]

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15 Apr 2017, 01:47
Answer is B.. Get is 1:24 should be less though
East coast*Mid coast*west coast
3c2*1c1*3c2
3*1*3
9
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Re: A retail company needs to set up five additional distribution centers  [#permalink]

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17 Apr 2017, 13:07
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
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Re: A retail company needs to set up five additional distribution centers  [#permalink]

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21 Apr 2017, 23:36
Bunuel wrote:
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
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Re: A retail company needs to set up five additional distribution centers  [#permalink]

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17 Sep 2017, 03:50
The management allocate the distribution centers in : 3C2 * 1C1 * 3C2 = 9

Bunuel : please provide the OA after review.
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Posts: 50627
Re: A retail company needs to set up five additional distribution centers  [#permalink]

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17 Sep 2017, 03:55
chipsy wrote:
The management allocate the distribution centers in : 3C2 * 1C1 * 3C2 = 9

Bunuel : please provide the OA after review.

________________
The OA is B.
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A retail company needs to set up five additional distribution centers  [#permalink]

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17 Sep 2017, 04:10
Nevernevergiveup wrote:

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.
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Re: A retail company needs to set up five additional distribution centers  [#permalink]

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30 Jan 2018, 12:52
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.

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Re: A retail company needs to set up five additional distribution centers &nbs [#permalink] 30 Jan 2018, 12:52
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