#### Question

In one state, automobile license plates must have two digits (no leading zeros) followed by one letter followed by a string of two to four digits (leading zeros are allowed). How many different plates are possible?

#### Solution

Verified#### Step 1

1 of 3Multiplication Principle

If there are $n_{1}$ possible outcomes for a first event

and $n_{2}$ possible outcomes for a second event,

there are $n_{1}\cdot n_{2}$ possible outcomes for the sequence of the two events.

${\it Addition Principle}$

If A and B are disjoint events with $n_{1}$ and $n_{2}$ possible outcomes, respectively,

then the total number of possible outcomes for event “A or B” is $n_{1}+n_{2}$.

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