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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?

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

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20 Jan 2015, 23:03

2

This post was BOOKMARKED

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.

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

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08 Feb 2015, 03:00

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.

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
_________________

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

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06 Apr 2016, 01:35

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

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,

..

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..

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

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12 Jul 2016, 05:03

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,

..

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..

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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02 Apr 2017, 10:58

1

This post was BOOKMARKED

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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17 Apr 2017, 14:07

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

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

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22 Apr 2017, 00:36

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-

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?

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.