Find Number of Passwords

[nycmathguy]

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?

Seeking a set up or several hints.

 

[MathLover1]

hint: Note that we are told that no digit may be repeated.
There are total of 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
As password must be at least 9 digits long then it can consist of either 9 or all 10 digits.
It's good to realize the permutation formula: n! / (n-k)!

 

[nycmathguy]

hint: Note that we are told that no digit may be repeated.
There are total of 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
As password must be at least 9 digits long then it can consist of either 9 or all 10 digits.
It's good to realize the permutation formula: n! / (n-k)!

Is the set up 9P10 or 10P9?

 

[MathLover1]

10! / (10-9)! = 10!/1! = 10!
and
10! / (10-10)! = 10!/0! = 10! = 10!/1! = 10!

The answer is than: 2 * 10!=7257600

 

[nycmathguy]

10! / (10-9)! = 10!/1! = 10!
and
10! / (10-10)! = 10!/0! = 10! = 10!/1! = 10!

The answer is than: 2 * 10!=7257600

Ok. The answer is 10P9.

I'm curious but why can't the answer be 9P10?