Calculate the number of possible combinations

Question

Given 4 sets of data, how can I find the number of possible combinations?

Eg.
Colors { Black, Blue, Red, Green }
Shape { Round, Square, Triangular }
Form { Solid, Liquid }
Location { Inside, Outside }

Empty or not selecting an item from a set is not an option. Therefore, { Black, Solid } is invalid but { Black, Square, Solid, Inside } would be valid.

I don't need to generate the list, I'm just curious as to how I'd go about calculating the number of possible combinations.

Answer 1

Just multiply together the ways to select from each set.

Answer 2

The number of total combinations are $4\cdot3\cdot2\cdot2$.

If you want to see by yourself why is that, try to draw a graph/tree: Put on the top the 4 different colors. For each color, create 3 childs for the shapes. For each shape, create 2 childs for the forms etc...

Fyi, if not selecting an item was an option, the answer would be $5\cdot4\cdot3\cdot3$. This is because in every set you should add the empty option.