Combinatorics Question

[hkparikh09]

The Carson family will purchase three used cars. There are two models of cars available, Model A and Model B, each of which is available in four colors: blue, black, red and green. How many different combinations of three cars can the Carsons select if all the cars are to be different colors.

I used a hybrid version of the slot method:

The first choice has 8 options (2 models x 4 colors)

2nd choice has 6 options (2 models x 3 colors)

3rd choice has 4 options (2 models x 2 colors)

My answer choice was 192 = 8 x 6 x 4

However the answer is 32. According to the MGMAT explanation, "the order in which the purchases are made is not important so we must divide by the factorial of the number of choices to eliminate over-counting."

Can someone please explain the last step (divide by the factorial)? I am not sure why it is necessary.

[jnelson0612]

Certainly! Check out this post on that question and then please let us know if we can answer further questions: the-carson-family-will-purchase-three-used-cars-there-are-t12659.html

[hkparikh09]

Thank you very much. That linked helped a lot. As a technical question, is there a way I can search the forum too see if my problem was already discussed? I'd hate to start duplicate threads.

[jpdelavin]

Here is another approach to this problem.

First, you can choose the colors that you will purchase. The number of ways of choosing 3 colors is 4C3 = 4.

Then, given a color, you have two models that you can choose from, A or B. Since there are three colors, 2*2*2 = 8.

4*8 = 32

[RonPurewal]

Thank you very much. That linked helped a lot. As a technical question, is there a way I can search the forum too see if my problem was already discussed? I'd hate to start duplicate threads.

the fastest way to search the forum (in my experience) is to type into google:
site:manhattangmat.com xxxxxx
or
site:manhattangmat.com/forums xxxxxx
(where "xxxx" is whatever you're searching the forum for).

that will restrict your search to things on our server -- and it's a heck of a lot faster than the search box that's actually on the forum.