A popular website requires users to create a password consisting of the digits {1,2,3,4,5,6,7}. If no digit may be repeated and each password must be at least 6 digits long, how many passwords are possible?
Choose the most appropriate option.
A) 6! + 7!  B) 2 x 7!  C) 6! x 7!  D) 13!  E) 14!
If we choose the 7 different digits then they can be arranged in 7! ways.   The number of possible 6-digit passwords is 7*6*5*4*3*2 = 7!   The total number of passwords is 7! + 7! = 2*7!   The answer is 2 x 7!.
<result>B</result>
A popular website requires users to create a password consisting of the digits {1,2,3,4,5,6,7}. If no digit may be repeated and each password must be at least 6 digits long, how many passwords are possible?