How do I calculate the number of different combinations of multiple sets' elements (different number of elements on each set)? First of all, I have no experience with mathematics, so my terminology may be wrong, but let me illustrate my question:
Let's say that I have 4 different sets of elements:
[apples, oranges, lemons]
[a, b, c, d, e]
[black, white, red, blue]
[1, 2]

I want to find how many different combinations of the items there are. Notice:


*

*The combinations will always have 1 item from every list

*The 1st item in every combination will be chosen from the 1st list, the 2nd from the 2nd etc.


So, basically the first 5 combinations would be:


*

*apples - a - black - 1

*apples - a - black - 2

*apples - a - white - 1

*apples - a - white - 2

*apples - a - red - 1


etc etc
Sorry for not putting it in mathematical terms but I hope you understand what I'm trying to ask.

Just multiply the number of elements in each step. This is called the rule of product.
To state it simply, if you have $a$ ways to select something from a set, and $b$ ways to select another from another set, you have $a \cdot b$ ways to select one element from each set. This also applies if you have more than 2 sets.
