How many different license plates can be formed if each plate has 1 digit followed by 5 different

This is a fundamental counting principle problem and can be solved by multiplying the number of choices you have for each digit of the license plate.

For the first digit you can choose from the numbers 0,1,2...,9 or 10 choices.
Now the next 5 digits will all be letters all being different.. recall there are 26 letters in the alphabet.. for our second digit we have 26 choices, for our third digit we have 25 choices(because we already used one of the 26 letters and we can't repeat), for our fourth digit we have 24 choices and well I'm sure you are catching on by now...

Here is what the whole calculation looks like:
10(26)(25)(24)(23)(22) = 78,936,000

Let me know if you have questions...hope this helped