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 three 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?	Choose the correct choice.
A) 24
B) 32
C) 8
D) 60
E) 192
I have no idea how you got 8C8, 7C6 and 4C1.   I could have understood 8C1*6C1*4C1 (I have explained why this doesn't work in the post above)   The best way to solve it is by first selecting 3 colors out of the given 4 in 4C3 ways. (say, you got black, red and green)   Now for each color, you have 2 choices - model A or B   So you select a model in 2 ways.   No of ways of selecting the 3 cars = 3C3 * 2 * 2 * 2 = 8   Well, my logic was   The number of ways of selecting r objects from n different objects is nCr.   We have 8 options and can select either of the 8 as the first - 888   One car is gone and one becomes a forbidden choice so we have 7 options and need to select either of the 6 as the first - 786   Two cars are gone and two becomes a forbidden choice so we have 6 options and need to select either of the 4 as the first - 684   8
<result>C</result>
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 three 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?