Q29. - Algebra 2

Question

WRITING IN MATH

Answer the question that was posed at the beginning of the lesson.

How can you count the maximum number of license plates a state can issue?

Include the following in your answer:

• an explanation of how to use the Fundamental Counting Principle to find the

number of different license plates in a state such as Florida, which has $3$ letters

followed by $3$ numbers, and

• a way that a state can increase the number of possible plates without

increasing the length of the plate number.

Step-by-Step Solution

Answer

• We have $26$choices for each letter at each place and we have  ten choices for each number
• Replace the order of license plate

Step 1. Given information

In Florida state, we have given a license plate with three letters and three numbers

Step 2. Concept used

We have $26$ choices for each letter at each place and we have ten choices for each number.

Reposition the numbers and letters.

Step 3. Calculation

The maximum number of license plates is a product with factors of $26 \text{s}$ and $10s$, depending on how many letters are used and how many digits are used.

There are 26 choices for the first letter, 26 for the second, and 26 for the third. There are 10 choices for the first number, 10 for the second, and 10 for the third. 

By the Fundamental Counting Principle,

There are ${26}^3\times {10}^3$or $17,576,000$ possible license plates.