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A retail company needs to set up

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by gmatdriller » Sat Nov 22, 2014 8:55 am
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

The question appears overly wordy.. Someone explain please
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by [email protected] » Sat Nov 22, 2014 10:23 am
Hi gmatdriller,

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

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by Brent@GMATPrepNow » Sat Nov 22, 2014 3:11 pm
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,
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Brent Hanneson - Creator of GMATPrepNow.com
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by gmatdriller » Sun Nov 23, 2014 7:32 am
Thanks Rich; I got it now.
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by conquistador » Tue Jul 12, 2016 3:59 am
[email protected] wrote:
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
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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by [email protected] » Tue Jul 12, 2016 12:01 pm
Hi Mechmeera,

Since we're choosing cities in GROUPS, it doesn't matter what the order is - as such, we're dealing with Combination "math." As an example, choosing Boston and New York is the same as choosing New York and Boston - so we can't count that option twice. You're approaching the math as if it were a Permutation (and if you want to do that, then that's okay, but you still have to mathematically 'remove' the duplicate options).

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