QuestionEach license plate in a certain state has six characters (with repeats allo
Here are the possibilities for each character.
\begin{tabular}{|c|l|}
\hline Character & \multicolumn{1}{|c|}{ Possibilities } \\
\hline First & The digits 1, 2, 3, 4, or 5 \\
\hline Second & The 26 letters of the alphabet \\
\hline Third & The 26 letters of the alphabet \\
\hline Fourth & The 10 digits 0 through 9 \\
\hline Fifth & The 10 digits 0 through 9 \\
\hline Sixth & The 10 digits 0 through 9 \\
\hline
\end{tabular}
How many license plates are possible in this state?
Studdy Solution
STEP 1
1. Each license plate consists of six characters.
2. Characters can repeat.
3. The first character can be one of the digits 1, 2, 3, 4, or 5.
4. The second and third characters can be any of the 26 letters of the alphabet.
5. The fourth, fifth, and sixth characters can be any of the 10 digits 0 through 9.
STEP 2
1. Determine the number of possibilities for each character.
2. Calculate the total number of possible license plates.
STEP 3
Determine the number of possibilities for each character: - First character: 5 possibilities (1, 2, 3, 4, or 5) - Second character: 26 possibilities (A to Z) - Third character: 26 possibilities (A to Z) - Fourth character: 10 possibilities (0 to 9) - Fifth character: 10 possibilities (0 to 9) - Sixth character: 10 possibilities (0 to 9)
STEP 4
Calculate the total number of possible license plates by multiplying the possibilities for each character:
STEP 5
Perform the multiplication:
The total number of possible license plates is:
Was this helpful?
