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

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Multiplication Principle

If there are n1n_{1} possible outcomes for a first event

and n2n_{2} possible outcomes for a second event,

there are n1n2n_{1}\cdot n_{2} possible outcomes for the sequence of the two events.

AdditionPrinciple{\it Addition Principle}

If A and B are disjoint events with n1n_{1} and n2n_{2} possible outcomes, respectively,

then the total number of possible outcomes for event “A or B” is n1+n2n_{1}+n_{2}.

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