How do I calculate the number of different combinations of multiple sets' elements (different number of elements on each set)?

combinatorics

Solution 1:

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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