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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.

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up vote 9 down vote accepted

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.

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