A retail company needs to set up 5 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 mid-west (Chicago), and three cities on
the west coast (Seattle, San Francisco and Los Angeles). If the company must have 2 distribution centers on
each coast and 1 in the mid-west, and only one center can be added in each city, in how many ways can the
management allocate the distribution centers?
OE [spoiler]3c2*1*3c2[/spoiler]
I thought (3c2*1*3C2)+(3c3*1*3c1)
whats wrong with my thinking???
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permutation nd combinations
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akash singhal
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Check my post here:akash singhal wrote:A retail company needs to set up 5 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 mid-west (Chicago), and three cities on
the west coast (Seattle, San Francisco and Los Angeles). If the company must have 2 distribution centers on
each coast and 1 in the mid-west, and only one center can be added in each city, in how many ways can the
management allocate the distribution centers?
https://www.beatthegmat.com/combination- ... 85034.html
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akash singhal
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Thanks MitchGMATGuruNY wrote:Check my post here:akash singhal wrote:A retail company needs to set up 5 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 mid-west (Chicago), and three cities on
the west coast (Seattle, San Francisco and Los Angeles). If the company must have 2 distribution centers on
each coast and 1 in the mid-west, and only one center can be added in each city, in how many ways can the
management allocate the distribution centers?
https://www.beatthegmat.com/combination- ... 85034.html
My mistake I misread the question.
It says 'each coast' nd i read 'east coast'
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Hi gmatdriller,
A) 3
B) 9
C) 18
D) 20
E) 36
To start, the original prompt includes the above 5 answer choices.
This question IS wordy, but 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: B
GMAT assassins aren't born, they're made,
Rich
A) 3
B) 9
C) 18
D) 20
E) 36
To start, the original prompt includes the above 5 answer choices.
This question IS wordy, but 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: B
GMAT assassins aren't born, they're made,
Rich
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Brent@GMATPrepNow
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Rich has provided a nice solution, so I won't rehash that here.
I will, however, say that there's a nice fast way to calculate combinations (like 3C1, 7C2, etc ) in your head.
Here's a free video that explains how: https://www.gmatprepnow.com/module/gmat-counting?id=789
Cheers,
Brent
I will, however, say that there's a nice fast way to calculate combinations (like 3C1, 7C2, etc ) in your head.
Here's a free video that explains how: https://www.gmatprepnow.com/module/gmat-counting?id=789
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
