Alice attends a small college in which each class meets only once a week. She is
deciding between 30 non-overlapping classes. There are 6 classes to choose from
for each day of the week, Monday through Friday. Trusting in the benevolence
of randomness, Alice decides to register for 7 randomly selected classes out of
the 30, with all choices equally likely. What is the probability that she will have
classes every day, Monday through Friday?
Seems like basic probability theory
The Attempt at a Solution
I'm confused here, because my thinking was that I should be able to say she can choose any course for the five days of the week (65 ways of doing this), and then any two of the remaining 25 courses (C(25,2) ways of doing this), so the total probability is 65*C(25,2) / C(30,7). But this is wrong (the answer is above 1).
I considered also that if, after she has picked one course on each day of the week (65), she can then pick another, she has 25 options, and then 24 more after that (since those are how many courses are available at each stage, and she can pick anything since she has fulfilled the every-day-class criterion). But this gives 65*25*24 / C(30,7) which is also wrong (above 1).
Why are these methods wrong?