Heres the question im stuck on...

A password with between 6 and 8 characters, each can be lowercase, uppercase, or any digit 0-9. A password must start with a letter and have atleast one digit. ex. How many passwords are possible?

Heres what I m thinking, but I have a feeling its more difficult than this...

for the first letter you would have 52 choices (upper plus lower) and also you require a digit for one (10 choices) the rest it could be any 62 choices (digits plus letters)

52 x 10 x 62 x 62 x 62 x 62 x 62 x 62... doesnt seem correct.. help if you can