Matt is designing a website authentication system. He knows passwords are most secure ifthey contain letters, numbers, and symbols. However, he doesn't quite understand that this additional

security is defeated if he speci es in which positions each character type appears. He decides that valid
passwords for his system will begin with three letters (uppercase and lowercase both allowed), followed
by two digits, followed by one of 10 symbols, followed by two uppercase letters, followed by a digit,
followed by one of 10 symbols. How many di erent passwords are there for his website system? How
does this compare to the total number of strings of length 10 made from the alphabet of all uppercase
and lowercase English letters, decimal digits, and 10 symbols?