license plates in a particular state display ...
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 different license plates that can be manufactured for this state. (simplify your answer. type an integer or a fraction.)
Answer
# Explanation:
## Step1: Determine number of choices for letters
There are 26 letters in the alphabet. For each of the 4 - letter positions, there are 26 choices. So the total number of ways to choose the 4 - letter part is $26\times26\times26\times26=26^{4}$ by the multiplication principle.
## Step2: Determine number of choices for numbers
There are 10 digits from 0 - 9. For each of the 2 - number positions, there are 10 choices. So the total number of ways to choose the 2 - number part is $10\times10 = 10^{2}$ by the multiplication principle.
## Step3: Calculate total number of license - plates
The total number of license plates is the product of the number of ways to choose the letter part and the number of ways to choose the number part. So the total number of license plates is $26^{4}\times10^{2}$.
$26^{4}=(26\times26)\times(26\times26)=676\times676 = 456976$, and $10^{2}=100$. Then $26^{4}\times10^{2}=456976\times100 = 45697600$.
# Answer:
45697600