If a new car has 2 transmission types, 3 vehicle styles, 3 option packages, 9 exterior color choices, and 3 interior color choices, how many different new cars are possible?
There are possible different cars.

To find the total number of different new cars possible, you would multiply the number of choices for each category. So, for this car:

2 transmission types × 3 vehicle styles × 3 option packages × 9 exterior color choices × 3 interior color choices = 2 × 3 × 3 × 9 × 3.

Calculating this gives us:

2 × 3 = 6
6 × 3 = 18
18 × 9 = 162
162 × 3 = 486.

Thus, there are 486 possible different cars.

Now, regarding how we got there! It’s like mixing ingredients to make a special recipe: each category adds a unique flavor ensuring every new car’s distinct from the others. Gone are the days of cookie-cutter vehicles; the combination of features makes each one as unique as a fingerprint!

And another neat point: this is a classic example of the fundamental principle of counting, which is used in many fields including statistics and computer science! So next time you’re pondering choices, remember this fun way of calculating how many combinations you can create!