A popular website requires users to create a password consisting of the digits {1,2,3,4,5,6,7,8}. If no digit may be repeated and each password must be at least 7 digits long, how many passwords are possible?
Choices:
A) 7! + 8!  B) 2 x 8!  C) 7! x 8!  D) 15!  E) 16!
If we choose the 8 different digits then they can be arranged in 8! ways.   The number of possible 7-digit passwords is 8*...*2 = 8!   The total number of passwords is 8! + 8! = 2*8!   The answer is 2 x 8!.
<result>B</result>
A popular website requires users to create a password consisting of the digits {1,2,3,4,5,6,7,8}. If no digit may be repeated and each password must be at least 7 digits long, how many passwords are possible?