permutation nd combinations

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akash singhal: Master | Next Rank: 500 Posts; Posts: 152; Joined: Fri Apr 24, 2015 1:39 amFollowed by: 3 members; Location: Rourkela Odisha India; Thanked: 2 times; GMAT Score:650

by akash singhal » Thu Nov 12, 2015 3:24 am

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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Source: Beat The GMAT — Problem Solving | Thu Nov 12, 2015 3:24 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Nov 12, 2015 3:32 am

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?

Check my post here:

https://www.beatthegmat.com/combination- ... 85034.html

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akash singhal: Master | Next Rank: 500 Posts; Posts: 152; Joined: Fri Apr 24, 2015 1:39 amFollowed by: 3 members; Location: Rourkela Odisha India; Thanked: 2 times; GMAT Score:650

by akash singhal » Thu Nov 12, 2015 3:50 am

GMATGuruNY wrote:
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?
Check my post here:

https://www.beatthegmat.com/combination- ... 85034.html

Thanks Mitch
My mistake I misread the question.
It says 'each coast' nd i read 'east coast'

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Thu Nov 12, 2015 9:27 am

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

Contact Rich at [email protected]

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu Nov 12, 2015 9:28 am

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

Brent Hanneson - Creator of GMATPrepNow.com

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