Question

Each license plate in a certain state has five characters (with repeats allowed).Here are the possibilities for each character.CharacterPossibilitiesFirstThe digits , , , , or SecondThe letters of the alphabetThirdThe letters of the alphabetFourthThe digits through FifthThe digits through How many license plates are possible in this state?

Answer 1

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SOLUTION

Given the information as contained in the image;

`\begin{gathered} Since\text{ repetition is allowed;} \\ The\text{ first character has 5 possible choices}\rightarrow5 \\ The\text{ second character has 26 possible choices}\rightarrow26 \\ The\text{ third character has 26 possibles choices}\rightarrow26 \\ The\text{ fourth character has 10 possible choices}\rightarrow10 \\ The\text{ fifth character has 10 posible choices}\rightarrow10 \end{gathered}`

To determine the number of possible license plates in the state;

`5*26*26*10*10=338000`

The answer is 338000.