A particular state's license plates have 7 characters. Each character can be a capital letter, or a digit except for 0. How many license plates are there in which no two adjacent characters are the same

N = 35 * 34^6

N = 54,068,154,560

Step-by-step explanation:

Given;

The license plate have 7 characters.

Each character can be a capital letter, or a digit except for 0.

There are 26 capital letters

And there are 9 digits excluding 0

The total number of possible entries in each character is;

26+9 = 35

The number of license plates in which no two adjacent characters are the same are;

For no two adjacent characters of the license plate not to be the same that is no two characters that follow each other can be the same, the number of possible entries in the adjacent characters apart from the first character would be reduced by one.

N = 35 * 34 * 34*34*34*34*34

N = 35 * 34^6

N = 54,068,154,560

Therefore, there are 54,068,154,560 possible license plates