permutation nd combinations

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

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