A computer system has n users, each with a unique name and password.

Due to a software error, the n passwords are randomly permuted internally $($i$.$e$.,$ each of

the n$!$ possible permutations is equally likely$).$ Only those users lucky enough to have

had their passwords unchanged in the permutation are able to continue using the system.

$($a$)$ What is the probability that a particular user, say user $1,$ is able to continue using

the system?

$($b$)$ What is the expected number of users able to continue using the system? Hint:

Let Xi be a rv with the value $1$ if user i can use the system and $0$ otherwise.