Questions: Each license plate in a certain state has six characters (with repeats allowed). Here are the possibilities for each character: - Character possibilities - First: The 26 letters of the alphabet - Second: The 26 letters of the alphabet - Third: The 26 letters of the alphabet - Fourth: The 10 digits 0 through 9 - Fifth: The 10 digits 0 through 9 - Sixth: The 10 digits 0 through 9 How many license plates are possible in this state?

Solution Steps

The license plate consists of six characters. The first three characters are letters, and the last three characters are digits. We need to determine the number of possibilities for each character:

• The first character can be any of the 26 letters of the alphabet.
• The second character can be any of the 26 letters of the alphabet.
• The third character can be any of the 26 letters of the alphabet.
• The fourth character can be any of the 10 digits (0 through 9).
• The fifth character can be any of the 10 digits (0 through 9).
• The sixth character can be any of the 10 digits (0 through 9).

To find the total number of possible license plates, we multiply the number of possibilities for each character:

\[ 26 \times 26 \times 26 \times 10 \times 10 \times 10 \]

Calculate the product:

\[ 26^3 = 26 \times 26 \times 26 = 17,576 \]

\[ 10^3 = 10 \times 10 \times 10 = 1,000 \]

Now, multiply these results:

\[ 17,576 \times 1,000 = 17,576,000 \]

Final Answer