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by g.shankaran » Tue May 31, 2011 10:12 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?

24

32

48

60

192
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by cans » Tue May 31, 2011 10:17 am
IMO B
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by g.shankaran » Tue May 31, 2011 10:18 am
Cans - Thanks can you please explain?
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by Frankenstein » Tue May 31, 2011 10:20 am
Hi,
Car1 can be selected from 8 cars in 8 ways
Car2 can be selected from 6 cars in 6 ways
Car3 can be selected from 4 cars in 4 ways
Order of the cars is unimportant. So, number of combinations is 8.6.4/3! = 32
(or)
Choose 3 colors from the 4 in 4C3 ways
For each color, we can choose either modelA or modelB in 2 ways.
So, number of combinations is 4C3.(2)^3 = 32

Hence, B

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by cans » Tue May 31, 2011 10:26 am
4 colors available. To select 3 cars with all different - 4C3 ways
for each color, 2 models. thus 2*2*2 =8
Total of 4C3*8 = 32
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