Derangement / Principle of Inclusion-Exclusion Question

[sakic19]

Hi, I was wondering if anyone could help me get started with this question:

6 groups of students each consisting of 9 students are in a theatre and sit in rows 1 to 6 and columns A to I, with all students in the same group sitting in the same row. All the students leave and come back, again sitting in rows 1 to 6 and columns A to I, all students in the same group are still sitting in the same row.

What is the probability that:

1. No group of students sits in its original row?
2. Exactly 2 groups of students sit in their original row?
3. At least 3 groups of students sit in their original row?
4. No students sit in their original row and no student sits in their original column?

Can anyone help me get started with this question, using the Principle of Inclusion-Exclusion?

Thanks!

[stapel_eliz]

Try here for one solution.