- #1

Astudious

- 61

- 0

## Homework Statement

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?

## Homework Equations

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 (6

^{5}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 6

^{5}*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 (6

^{5}), 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 6

^{5}*25*24 / C(30,7) which is also wrong (above 1).

Why are these methods wrong?