# Rule of Product

The Rule of Product goes by other names such as the Multiplication Principle or Sequential Rule. It is a multiplication based rule one follows in certain counting procedures.

“The rule of product states that if an action can be performed by making $$A$$ choices followed by $$B$$ choices, then it can be performed $$AB$$ ways” (Benjamin, 2009).

In other words suppose there exists a set of $$A$$ choices and a set $$B$$ choices, multiplying $$AB$$ will be the number of ways to do $$A$$ and $$B$$. As a side note, notice the word “and”, this can often be a queue word for situations were one might find need for The Rule of Product.

Independence of a sets is also required when The Rule of Product is in play. That simply means that a set $$A$$ and set $$B$$ from earlier are completely separate.

Moreover, this rule extends to any number of sets. Meaning if we have a set $$A$$, $$B$$, $$C$$, and $$D$$ they can still be multiplied $$ABCD$$.

So lets look at a simple example.

Say there is a 3 dial combination lock where each dial is completely separate and each contain the numbers 0 through 9. How many possible combinations can be made between the first, second, and third dials?