I have been super stuck on this problem for a while and thought I turn to some expert help. My problem question:
A password has length $8$ with a mix of $1$ uppercase letter (from $A$..$Z$), $5$ lowercase letters (from $a$...$z$) and $2$ digits (from $0$...$9$). Bob is trying to guess the password and does not know in which order these characters occur in the password.
Suppose that all characters in the password are different and Bob discovers the position of the lowercase letters and one of them is $'w'$(without knowing which one). Bob then writes a program that repeatedly chooses one of the possible passwords uniformly at random, and tries it.
The program tries $6000$ trials per second. What is the expected value of the number of minutes until Bob guesses the password?
I have an inkling that this is related to Bernoulli trials and/or geometric distribution but I don't know where and how to start. Please help.