CPM Homework Help : CCG Problem 10-132

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

Step 1:

Since repetition is allowed, the total number of license plates of the first type is
$26\cdot26\cdot26\cdot10\cdot10\cdot10 = 17,576,000$ .

Step 2:

The total number of license plates of the second type is
$9\cdot26\cdot26\cdot26\cdot10\cdot10\cdot10 = 158,184,000$ .

Find the difference.

Step 3:

Find the number of license plates containing $\text{ALG }2$ .

$9\cdot1\cdot1\cdot1\cdot1\cdot10\cdot10 =$

Step 4:

$P(\text{ALG }2)=\frac{900}{158,184,000}=?$