You have been named Secretary of Transportation for the State of [Your Favorite State]. Congratulations! You’re considering replacing the current license plate format ABCD XXXXXXXXXXletters followed...

You have been named Secretary of Transportation for the State of [Your Favorite State]. Congratulations! You’re considering replacing the current license plate format ABCD-1234 (4 letters followed by 4 digits) with a sequence of any k symbols, each of which can be either a letter or a digit. How large must k be so that your new format has at least as many options as the old format did?