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?
a) 24
b) 32
c) 48
d) 60
e) 192
I'm having just a little difficulty understanding this problem. I know to use the slot method and that there are a total of 8 different model cars (2*4).
I also understand the slot method is 8 * 6* 4. What I don't understand is why I need to divide by 3!.
The explanation says order doesn't matter, but I didn't think about that in when I was reading the problem. Can someone help me know when I should or shouldn't be dividing by the number of choice I'm making in such a problem?