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 seven 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? Select the correct option:  A) 24  B) 32  C) 48  D) 254  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 = 7C3 * 2 * 2 * 2 = 254   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 - 8C8   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 - 7C6   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 - 6C4   254
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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 seven 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?