Question

Buick automobiles come in four models, 12 colors, three engine sizes, and two transmission types. (a) How many distinct Buicks can be manufactured? (b) If one of the available colors is blue, how many different blue Buicks can be manufactured?

Answer 1

For the first part I was able to get 288 using permutations(since we are asked for a distinct number of Buicks, and the order is important).
\[4\times 12 \times 3\times 2 = 288\]
where each number represents the model, color, engine, and transmission types you can choose from.

Answer 2

For the second part I got 24 using a smiilar method like the above one except now I've accounted for the distinct color blue:
\[4 \times 1 \times 3 \times 2 = 24\]
where each number represents the model, the color blue, engine, and transmission types you can choose from.


I know my answers are right because thats what my book got, I just want to know if my reasoning behind these answers is correct.