You know you have the 5 color choices, then you can select one color from given five in 5 ways (here you use combination, because the order doesn't "matters"). Also you know that there are 8 different options and you have to select two options, you can choose them in
[tex] C_8^2=\dfrac{8!}{2!(8-2)!}=\dfrac{8!}{2!\cdot 6!}=\dfrac{1\cdot 2\cdot 3\cdot 4\cdot 5\cdot 6\cdot 7\cdot 8}{1\cdot 2\cdot 1\cdot 2\cdot 3\cdot 4\cdot 5\cdot 6} =\dfrac{7\cdot 8}{2} =28 [/tex] ways (here you use combination too, because the order doesn't "matters" too).
Use the product rule to count the totl number of choices: 5·28=140 ways to select a new car for you.
You want a black car with air conditioning and a sun roof. This is one choice from 140 possible choices, then the probability that your parents will make the same choice is 1/140.
