Austin Warby edited The_Rule_of_Product_goes__.tex  about 8 years ago

Commit id: 23b4e0f476b67b740857a768fb02db6c06de5c70

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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 2 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 first, second,  and second third  dials? Before moving forward we should first identify our sets. We will call the first dial's 0 through 9 digits set $A$. We will call the second dial's 0 through 9 digits set $B$. Are We will call  the two third dial's 0 through 9 digits  set $C$. Are the three sets  independent? Yes they are.