\problemdata
{counting}
{password}
{s01-ps7}

\begin{problem}

A certain company wants to have security for their computer
systems.  So they have given everyone a name and password.  The 
passwords are exactly 10 letters long.

\begin{problemparts}

\problempart If all the passwords must satisfy the following rules, how many
possible passwords are there :
\begin{enumerate}
\item[1.] The passwords must be permutations of the 
    letters (a, d, f, i, l, o, p, r, s, t)
\item[2.] No password can contain the sequence "fail"
\item[3.] No password can contain the sequence "drop"
\end{enumerate}

\problempart Bob is trying to break into the system.  He has obtained
the list of all the passwords and the list of all the names, yet he
doesnt know which passwords go with which names.  If the password file
contains 100 passwords and there are a 100 names, 
how many possible ways can those passwords be
associated with the names? Approximate your answer using Stirling's
approximation.

\probelmpart When trying to break into the system, Bob doesn't have to
submit an entire matching of the 100 user names with the 100 passwords
at the same time. Instead, he can try individual pairs of names and
passwords, i.e., he can try to login as any of the 100 users with any
of the 100 passwords and see if the login attempt is successful.

Describe a (good) strategy that Bob can use to completely determine
the pairing of names with passwords. How many login attempts does Bob
need to determine the entire matching in the worst case?

\end{problemparts}
\end{problem}

