Suppose there are 20 problems on the site the Sunday evening a user looks at the site the first time. She doesn't read the newest problem of the day, but instead ONLY reads problems that come up on the "Random Problem" page. She reads 5 random problems each day, always in the evening. The only problem is she can see the same problem more than once.

The other problem is problems continue to come in from the infinite queue. Two per week day and one per weekend.

What is the probability she will have read all the problems after her next Sunday evening check? What is the probability she will have read all the problems after the Sunday evening after that?

Note: The problems displayed when you click on "Random Problem" are independent of each other. There isn't anything to make sure that you are getting five different problems if you click on random problem five times.