Question

Camila sets up a passcode on her tablet, which allows only nine-digit codes. A spy sneaks a look at Camila's tablet and sees her fingerprints on the screen over nine numbers. What is the probability the spy is able to unlock the tablet on his first try? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

Answer 1

Since the password must be 9 digits long and the spy notices that Camila used 9 different digits, then, the probability that the spy unlocks the tablet on the first try is equal to 1 over the total amount of different ways in which 9 digits can be ordered (the spy knows the 9 digits that form the password but he does not know the order in which they should appear).

In general, there are n! ways of ordering a set with n elements.

Then, the total amount of different sequences that can be built using 9 digits is:

`9!=9*8*7*6*5*4*3*2*1=362,880`

Therefore, the probability that the spy unlocks the tablet on his first try is:

`(1)/(362880)`