Question

license plates in a particular state display 4 letters followed by 2 numbers. how many different license plates can be manufactured for this state? there are \\(\square\\) different license plates that can be manufactured for this state. (simplify your answer. type an integer or a fraction.)

Explanation:

Step1: Determine letter choices

There are 26 letters in the alphabet. For each of the 4 letter positions, there are 26 choices. So the number of ways to choose the 4 letters is $26\times26\times26\times26 = 26^4$.

Step2: Determine number choices

There are 10 digits (0 - 9). For each of the 2 number positions, there are 10 choices. So the number of ways to choose the 2 numbers is $10\times10 = 10^2$.

Step3: Calculate total license plates

By the multiplication principle, the total number of different license plates is the product of the number of letter combinations and number combinations. So we calculate $26^4\times10^2$.
First, $26^4 = 26\times26\times26\times26 = 456976$.
Then, $10^2 = 100$.
Multiplying these together: $456976\times100 = 45697600$.

Answer:

45697600