Probability of Broken Computers A school orders  7 new computers for a classroom but they are told 3 will not work properly when they recieve them.  The school begins to turn each computer on, one by one, to figure out which computers do not work.
There are quite a few questions but most of them I am just having trouble setting up and I feel mostly are similar in set up.

What is the probability that no more than five computers need to be turned on to find the three computers that don't work?

For this question N is the event the computer does not work and W means it works:
\begin{align}&\color{white}=P(NNN)+P(NWNN)+P(NWWNN)\\&=\left(\frac{3}{7}\cdot\frac{2}{6}\cdot\frac{1}{5}\right)\left(3\cdot\frac{1}{4}\cdot\frac{2}{6}\cdot\frac{4}{5}\cdot\frac{1}{4}\right)\left(4\cdot\frac{3}{7}\cdot\frac{2}{6}\cdot\frac{4}{5}\cdot\frac{3}{4}\cdot\frac{1}{3}\right)\\
&=\frac{12}{42875}\end{align}
The next couple questions are very similar I just don't know how to set up.  These all don't have specific order of which computers are picked but are told the computers are turned on in a couple possible spots.  These are the remaining questions if someondy can explain how these can be set up that be appreciated.

Given that exactly one of the computers not working was found within the first three computers, what is the probability that the other two computers that aren't wokring are found within the next three computers turned on?
Given that exactly two of the computers that don't work were found within the first three computers, what is the probability the last computer that doesn't work is found within the next two computers turning on?
Given that exactly two of the computers that don't work were found within the computers 1, 3, 5, what is the probability the other computer not working was found on tests 6 or 7?
Given the last computer doesn't work was found within the last two tests, what is the probability that the first two computers that don't work were found within the first three computers?


For the first question, it helps to consider the opposite event. What is the probability that more than five computers need to be turned on to find the three that do not work? In other words, what is the probability that after knowing the state of five computers, you still don't know the state of the two remaining computers?
Note that it really doesn't matter in which order the first five computers work or do not work.
