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by sparkle6 » Mon Oct 03, 2011 6:41 am
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


[spoiler]Answer: B[/spoiler]
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by knight247 » Mon Oct 03, 2011 6:48 am
For Car 1: We have 2 models to choose from and 4 colours to choose from. So 4*2=8
For Car 2: We have 2 models to choose from and 3 colours as we have to exclude the colour selected for car 1. So 2*3=6
For Car 3: We have 2 models to choose from and 2 colours as we have to exclude the previously selected colours. So 2*2=4

Combining all three we have 8*6*2=192
However, we have also considered ordered pairs in the above selections so we divide 192 by 3! i.e. 6
192/6=32 Hence B
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by gmatboost » Mon Oct 03, 2011 10:08 am
Or:

First choose the 3 colors: [spoiler]4C3= 4[/spoiler]
Next, for each of the three colors, [spoiler]there are two options (A and B)[/spoiler]

So the total number of possibilities is[spoiler] 4 * 2 * 2 * 2 = 32[/spoiler]
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