Question

1. license plates one state requires license plates to consist of three letters followed by three numbers. the letter \o\ and the number \0\ may not be used, but any other combination of letters or numbers is allowed. how many different license plates can be created?

Explanation:

Step1: Determine letter choices

There are 26 letters in the alphabet, and we exclude "O", so there are \(26 - 1 = 25\) choices for each of the three letter positions.

Step2: Determine number choices

There are 10 digits (0 - 9), and we exclude "0", so there are \(10 - 1 = 9\) choices for each of the three number positions.

Step3: Calculate total combinations

For the letters, the number of combinations is \(25\times25\times25\) (since each of the three letter positions has 25 choices). For the numbers, it's \(9\times9\times9\) (each of the three number positions has 9 choices). The total number of license plates is the product of these two, so \(25^3\times9^3\).
First, calculate \(25^3 = 25\times25\times25 = 15625\).
Then, calculate \(9^3 = 9\times9\times9 = 729\).
Now, multiply them: \(15625\times729 = 11390625\).

Answer:

11390625