### Home > INT2 > Chapter 12 > Lesson 12.2.3 > Problem12-102

12-102.

In the past, many states had license plates composed of three letters followed by three digits ($0$ to $9$). Recently, many states have responded to the increased number of cars by adding one digit ($1$ to $9$) ahead of the three letters. How many more license plates of the second type are possible? With the new system, what is the probability of being randomly assigned a license plate containing INT 2?

Since repetition is allowed, the total number of license plates of the first type is
$26 · 26· 26 · 10· 10 · 10 = 17{,}576{,}000$.

The total number of license plates of the second type is
$9 · 26 · 26 · 26 · 10 · 10 · 10 = 158{,}184{,}000$.

Find the difference.

Find the number of license plates containing INT2.

$9 · 1 · 1 · 1 · 1 · 10 · 10 =$

$P(INT2) = \frac{900}{158,184,000} = ?$