A popular website requires users to create a password consisting of digits only. If no digit may be repeated and each password must be at least 9 digits long, how many passwords are possible?
Choose the correct choice from the following options
A) 9! + 10!  B) 2 x 10!  C) 9! x 10!  D) 19!  E) 20!
If we choose the 10 different digits then they can be arranged (permutations) in 10! ways.   But the question asks at least 9 digits. So we have the possibility of choosing only 9 digits for the password ( but digit shouldn't repeat), so we can have a total of 10 different combinations and each combination can be arranged in 9! ways.   Therefore   10 x 9! + 10!   = 10! + 10!   = 2 x 10!   Therefore 2 x 10!
<result>B</result>
A popular website requires users to create a password consisting of digits only. If no digit may be repeated and each password must be at least 9 digits long, how many passwords are possible?